Complete Guide to Fractions and Ratios in ACT Math

Complete Guide to Fractions and Ratios in ACT Math SAT / ACT Prep Online Guides and Tips Fractions and ratios (and by extension rational numbers) are all around us and, knowingly or not, we use them every day. If you wanted to brag over the fact that you ate half a pizza by yourself (and why not?) or you needed to know how many parts water to rice you need when making rice on the stove (two parts water to one part rice), then you need to communicate this using fractions and ratios. In essence, fractions and ratios represent pieces of a whole by comparing those pieces either to each other or to the whole itself. Don’t worry if that sentence makes no sense right now. We’ll break down all the rules and workings of these concepts throughout this guideboth how these mathematical concepts work in general and how they will be presented to you on the ACT. Whether you are an old hat at dealing with fractions, ratios, and rationals, or a novice, this guide is for you. This guide will break down what these terms mean, how to manipulate these kinds of problems, and how to answer the most difficult fraction, ratio, and rational number questions on the ACT. What are Fractions? $${\a\piece}/{\the\whole}$$ Fractions are pieces of a whole. They are expressed as the amount you have (the numerator) over the whole (the denominator). Amy’s cat gave birth to 8 kittens. 5 of the kittens had stripes and 3 had spots. What fraction of the litter had stripes? $5/8$ of the litter had stripes. 5 is the numerator (top number) because that was the amount of striped kittens, and 8 is the denominator (bottom number) because there are 8 kittens total in the litter (the whole). Kitten math is the best kind of math. Special Fractions There are several different kinds of "special fractions" that you must know in order to solve the more complex fraction problems. Let us go through each of these: A number over itself equals 1 $6/6 = 1$ $47/47 = 1$ ${xy}/{xy} = 1$ A whole number can be expressed as itself over 1 $17 = 17/1$ $108 = 108/1$ $xy = {xy}/1$ 0 divided by any number is 0 $0/0 = 0$ $0/5 = 0$ $0/{xy} = 0$ Any number divided by 0 is undefined Zero cannot act as a denominator. For more information on this check out our guide to advanced integers. But, for now, all that matters is that you know that 0 cannot act as a denominator. Now let's find out how to manipulate fractions until we unlock the answers we want. Reducing Fractions If you have a fraction in which both the numerator and the denominator can be divided by the same number (called a â€Å"common factor†), then the fraction can be reduced. Most of the time, your final answer will be presented in its most reduced form. In order to reduce a fraction, you must find the common factor between each piece of the fraction and divide both the numerator and the denominator by that same amount. By dividing both the numerator and the denominator by the same number, you are able to maintain the proper relationship between each piece of your fraction. So if your fraction is $5/25$, then it can be written as $1/5$. Why? Because both 5 and 25 are divisible by 5. $5/5 = 1$ And $25/5 = 5$. So your final fraction is $1/5$. Adding or Subtracting Fractions You can add or subtract fractions as long as their denominators are the same. To do so, you keep the denominator consistent and simply add the numerators. $2/ + 6/ = 8/$ But you CANNOT add or subtract fractions if your denominators are unequal. $2/ + 4/5 = ?$ So what can you do when your denominators are unequal? You must make them equal by finding a common multiple (number they can both multiply evenly into) of their denominators. $2/ + 4/5$ Here, a common multiple (a number they can both be multiplied evenly into) of the two denominators 5 is 55. To convert the fraction, you must multiply both the numerator and the denominator by the amount the denominator took to achieve the new denominator (the common multiple). Why multiply both? Just like when we reduced fractions and had to divide the numerator and denominator by the same amount, now we must multiply the numerator and denominator by the same amount. This process keeps the fraction (the relationship between numerator and denominator) consistent. To get to the common denominator of 55, $2/$ must be multiplied by $5/5$. Why? Because $ * 5 = 55$. $(2/)(5/5) = 10/55$. To get to the common denominator of 55, $4/5$ must be multiplied by $/$. Why? Because $5 * = 55$. $(4/5)(/) = 44/55$. Now we can add them, as they have the same denominator. $10/55 + 44/55 = 54/55$ We cannot reduce $54/55$ any further as the two numbers do not share a common factor. So our final answer is $54/55$. Here, we are not being asked to actually add the fractions, just to find the least common denominator so that we could add the fractions. Because we are being asked to find the least amount of something, we should start at the smallest number and work our way down (for more on using answer choices to help solve your problem in the quickest and easiest way, check out our article on plugging in answers). Answer choice A is eliminated, as 40 is not evenly divisible by 12. 120 is evenly divisible by 8, 12, and 15, so it is our least common denominator. So our final answer is B, 120. Multiplying Fractions Luckily it is much simpler to multiply fractions than it is to add or divide them. There is no need to find a common denominator when multiplyingyou can just multiply the fractions straight across. To multiply a fraction, first multiply the numerators. This product becomes your new numerator. Next, multiply your two denominators. This product becomes your new denominator. $2/3 * 3/4 = (2 * 3)/(3 * 4) = 6/12$ And again, we reduce our fraction. Both the numerator and the denominator are divisible by 6, so our final answer becomes: $1/2$ Special note: you can speed up the multiplication and reduction process by finding a common factor of your cross multiples before you multiply. $2/3 * 3/4$ = $1/1 * 1/2$ = $1/2$. Both 3’s are multiples of 3, so we can replace them with 1 ($3/3 = 1$). Our other cross multiples are 2 and 4, which are both multiples of 2, so we were able to replace them with 1 and 2, respectively ($2/2 = 1$ and $4/2 = 2$). Because our cross multiples had factors in common, we were able to reduce the cross multiples before we even began. This saved us time in reducing the final fraction at the end. Take note that we can only reduce cross multiples when multiplying fractions, never while adding or subtracting them! It is also a completely optional step, so do not feel obligated to reduce your cross multiplesyou can always simply reduce your fraction at the end. Dividing Fractions In order to divide fractions, we must first take the reciprocal (the reversal) of one of the fractions. Afterwards, we simply multiply the two fractions together as normal. Why do we do this? Because division is the opposite of multiplication, so we must reverse one of the fractions to turn it back into a multiplication question. ${1/3} à · {3/8} = {1/3} * {8/3}$ (we took the reciprocal of $3/8$, which means we flipped the fraction upside down to become $8/3$) ${1/3} * {8/3} = 8/9$ Now that we've seen how to solve a fraction problem the long way, let's talk short cuts. Decimal Points Because fractions are pieces of a whole, you can also express fractions as either a decimal point or a percentage. To convert a fraction into a decimal, simply divide the numerator by the denominator. (The $/$ symbol also acts as a division sign) $3/10 = 3 + 10 = 0.3$ Sometimes it is easier to convert a fraction to a decimal in order to work through a problem. This can save you time and effort trying to figure out how to divide or multiply fractions. This is a perfect example of a time when it might be easier to work with decimals than with fractions. We’ll go through this problem both ways. Fastest waywith decimals: Simply find the decimal form for each fraction and then compare their sizes. To find the decimals, divide the numerator by the denominator. $5/3 = 1.667$ $7/4 = 1.75$ $6/5 = 1.2$ $9/8 = 1.125$ We can clearly see which fractions are smaller and larger now that they are in decimal form. In ascending order, they would be: $1.125, 1.2, 1.667, 1.75$ Which, when converted back to their fraction form, is: $9/8, 6/5, 5/3, 7/4$ So our final answer is A. Slower waywith fractions: Alternatively, we could compare the fractions by finding a common denominator of each fraction and then comparing the sizes of their numerators. Our denominators are: 3, 4, 5, 8. We know that there are no multiples of 4 or 8 that end in an odd number (because an even number * an even number = an even number), so a common denominator for all must end in 0. (Why? Because all multiples of 5 end in 0 or 5.) Multiples of 8 that end in 0 are also multiples of 40 (because $8 * 5 = 40$). 40 is not divisible by 3 and neither is 80, but 120 is. 120 is divisible by all four digits, so it is a common denominator. Now we must find out how many times each denominator must be multiplied to equal 120. That number will then be the amount to which we multiply the numerator in order to keep the fraction consistent. $120/3 = 40$ $5/3$ = ${5(40)}/{3(40)}$ = $200/120$ $120/4 = 30$ $7/4$ = ${7(30)}/{4(30)}$= $210/120$ $120/5 = 24$ $6/5$ = ${6(24)}/{5(24)}$= $144/120$ $120/8 = 15$ $9/8$ = ${9(15)}/{8(15)}$= $135/120$ Now that they all share a common denominator, we can simply look to the size of their numerators and compare the smallest and the largest. So the order of the fractions from least to greatest would be: $135/120, 144/120, 200/120, 210/120$ Which, when converted back into their original fractions, is: $9/8, 6/5, 5/3, 7/4$ So once again, our final answer is A. As you can see, we were able to solve the problem using either fractions or decimals. How you chose to approach these types of problems is completely up to you and depends on how you work best, as well as your time management strategies. Percentages After you convert your fraction to a decimal, you can also turn it into a percentage (if the need arises). To get a percentage, multiply your decimal point by 100. So 0.3 can also be written as 30%, because $0.3 * 100 = 30$. 0.01 can be written as 1% because $0.01 * 100 = 1$, etc. Be mindful of your decimals and percentages and don't mix them up! 0.1 is NOTthe same thing as 0.1%. Mixed Fractions Sometimes you may be given a mixed fraction on the ACT. A mixed fraction is a combination of a whole number and a fraction. For example, $5{1/3}$ is a mixed fraction. We have a whole number, 5, and a fraction, $1/3$. You can turn a mixed fraction into an ordinary fraction by multiplying the whole number by the denominator and then adding that product to the numerator. The final answer will be ${\the \new \numerator}/{\the \original \denominator}$. $5{1/3}$ $(5)(3) = 15$ $15 + 1 = 16$ So your final answer = $16/3$ You must convert mixed fractions into non-mixed fractions in order to multiply, divide, add, or subtract them with other fractions. A cobbler charges a flat fee of 45 dollars plus 75 dollars per hour to make a pair of shoes. How many hours of labor was spent making the shoes if the total bill was $320? $3{2/15}$ $3{2/3}$ $4$ $4{4/15}$ $4{1/3}$ If the total bill was 320 dollars and the flat fee was 45 dollars, we must subtract the flat fee from the total bill in order to find the number of hours the cobbler worked. $320 - 45 = 275$ So the cobbler worked 275 dollars’ worth of hours. In order to find out how many hours that is, we must divide the earnings by the hourly fee. $275/75 = 3{50/75}$ 75 was able to go evenly into 225, leaving 50 out of 75 left over. Because 50 and 75 share a common denominator of 25, we can reduce $3{50/75}$ to: $3{2/3}$ So our final answer is B, $3{2/3}$ Now that we've broken down all there is to knowabout ACT fractions, let's take a look attheir close cousinthe ratio. What are Ratios? Ratios are used as a way to compare one thing to another (or multiple things to one another). If Piotr has exactly 2 grey scarves and 7 red scarves in a drawer, the ratio of grey scarves to red scarves is 2 to 7. Expressing Ratios Ratios can be written in three different ways: $A \to B$ $A:B$ $A/B$ No matter which way you write them, these are all ratios comparing A to B. Most all chemical molecules are namedfor their ratios. Here, one of our products iscarbon dioxide (one part carbon, two parts oxygen). Different Types of Ratios Just as a fraction represents a part of something out of a whole (written as: ${\a \part}/{\the \whole}$), a ratio can be expressed as either: ${\a \part}:{\a \different \part}$ OR $\a \part:\the \whole$ Ratios compare values, so they can either compare individual pieces to one another or an individual piece to the whole. If Piotr has exactly 2 grey scarves and 7 red scarves in a drawer, the ratio of grey scarves to all the scarves in the drawer is 2 to 9. (Why 9? Because there are 2 grey and 7 red scarves, so together they make $2 + 7 = 9$ scarves total.) Reducing Ratios Just as fractions can be reduced, so too can ratios. Danielle collects toy racecars. 12 of them are blue and 4 of them are yellow. What is the ratio of of blue cars to yellow cars in her collection? Right now, the ratio is $12:4$. But they have a common denominator of 4, so this ratio can be reduced. $12/4 = 3$ $4/4 = 1$ So the carshave a ratio of $3:2$ Increasing Ratios Because you can reduce ratios, you can also do the opposite and increase them. In order to do so, you must multiply each piece of the ratio by the same amount (just as you had to divide by the same amount on each side to reduce the ratio). So the ratio of $3:2$ can also be $3(2):2(2) = 6:4$ $3(3):2(3) = 9:6$ $3(4):2(4) = 12:8$ And so on. Though this presents itself as a geometry problem, we don’t need to know any geometry in order to solve itwe only need to know about ratios. We have two triangles in a ratio of 2:5 and the smaller triangle has a hypotenuse of 5 inches. This means that we need to increase each side of the ratio by the amount it takes 2 to go into 5. $5/2 = 2.5$ So we must increase each side of the ratio by a matter of 2.5 $2(2.5):5(2.5)$ $5:12.5$ Our new, increased ratio is 5:12.5, which means that the larger hypotenuse is 12.5. Our final answer is K. Expand ratios, reduce themgo wild! Finding the Whole If you are given a ratio comparing two parts ($\piece:\another \piece$), and you are told to find the whole amount, simply add all the pieces together. It may help you to think of this like an algebra problem wherein each side of the ratio is a certain multiple of x. Because each side of the ratio must always be divided or multiplied by the same amount to keep the ratio consistent, we can think of each side as having the same variable attached to it. For example, a ratio of $6:7$ can be: $6(1):7(1) = 6:7$ $6(2):7(2) = 12:14$ And so on, just as we did above. But this means we could also represent $6:7$ as: $6x:7x$ Why? Because each side must change at the same rate. And in this case, our rate is $x$. So if you were asked to find the total amount, you would add the pieces together. $6x + 7x = 13x$. The total amount is $13x$. In this case, we don’t have any more information, but we know that the total MUST beeither 13 or any number divisible by 13. So let’s take a look at another problem. Clarissa has a jewelry box with necklaces and bracelets. The necklaces and bracelets are in a ratio of 4:3. What is NOT a possible number of total pieces of jewelry Clarissa can have in the box? 12 28 84 2 140 In order to find out how many pieces of jewelry she may have total, we must add the two pieces of our ratio together. So $4x + 3x = 7x$ This means that the total number of jewelry items in the box has to either be 7 or any multiple of 7. Why? Because $4:3$ is the most reduced form of the ratio of jewelry items in the box. This means she could have: $4(1):3(1) = 7$ jewels in the box (7 jewelry pieces total) $4(2):3(2) = 8:6$ jewels in the box (14 jewelry pieces total) $4(3):3(3) = 12:9$ jewels in the box (21 jewelry pieces total) And so forth. We don’t know exactly how many jewelry items she has, but we know that it must be a multiple of 7. This means our answer is A, 12. There is no possible way that she can have 12 jewels in the box, because 12 is not a multiple of 7 and one cannot have half a bracelet (unless something has gone terribly wrong). You may also be asked to find the number of individual pieces in your ratio after you are given the whole. This is exactly the opposite of what we did above. The is the exact same process as finding the whole, but in reverse. We know we must add the pieces of our ratio to find our multiple of 30. And we also know our ratio is $2:3$. So let us add these together. $2x + 3x = 5x$ Together, our ratio components add up to $5x$. And there are 30 feet total. So: $30/5 = 6$ $x = 6$ This means that we must multiply each side of our ratio by 6 in order to get the exact amount of wood used. This means that each piece is: $2(6):3(6)$ $12:18$ Which means our shorter piece is 12 feet long. Our final answer is H, 12. And now we come to rational and irrational numbers. Rational and Irrational Numbers A rational number is any number that can be written as a fraction of two integers (where the denominator does NOT equal to 0). All other numbers are considered irrational. Rational Numbers: $7/2, 5, 1/212, 0.66666667$ Why is 5 a rational number? Because it can be expressed as the fraction $5/1$. Why is 0.6666667 a rational number? Because it can be expressed as the fraction $2/3$ Irrational Numbers: $Ï€, √2, √3$ Why is $Ï€$ irrational? Because there is no fraction of two integers that can properly express it (through 22/7 comes awfully close). (Hint: if the decimals continue on forever without repeating, the number is irrational) Here, we are being asked to find the single rational number. Even if you didn’t know what a rational number meant, you might be able to figure this problem out just by finding the answer choice that stands out the most. But since you DO know what rational and irrational numbers are, it makes the problem even easier. Many square roots are irrational (unless they are roots of perfect squares like $√16 = 4$). We can immediately eliminate answer choices A, B, and C, as they are not perfect squares and so are irrational. We can also eliminate answer choice D. When we reduce the fraction, we get $√{1/5}$, and this would also get us an irrational number. This leaves us with answer choice E. We can see that both the numerator and the denominator of the fraction $64/49$ inside the square root sign are perfect squares. Since the fraction is under the root sign, let us take the square root of each of these. So our final fraction would look like: $√{64/49}$ = $8/7$ Because our final fraction is represented as a fraction with two integers, this is a rational number. So our final answer is E. So let's break down how to solve these kinds of questions when they show up on the test. How to Solve Fraction, Ratio, and Rational Number Questions When you are presented with a fraction or ratio problem, take note of these steps to find your solution: 1) Identify whether the problem involves fractions or ratios A fraction will involve the comparison of a $\piece/\whole$. A ratio will almost always involve the comparison of a $\piece:\piece$ (or, very rarely, a $\piece:\whole$). You can tell when the problem is ratio specific as the question text will do one of three things: Use the : symbol, Use the phrase â€Å"___ to ___† Explicitly use the word â€Å"ratio† in the text. If the questions wants you to give an answer as a ratio comparing two pieces, make sure you don’t confuse it with a fraction comparing a piece to the whole! 2) If a ratio question asks you to change or identify values, first find the sum of your pieces In order to determine your total amount (or the non-reduced amount of your individual pieces), you must add all the parts of your ratio together. This sum will either be your complete whole or will be a factor of your whole, if your ratio has been reduced. 3) When in doubt try to use decimals Decimals can make it much easier to work out problems rather than using fractions. So do not be afraid to convert your fractions into decimals to get through a problem more quickly and easily. 4) Remember your special fractions Always remember that a number over 1 is the same thing as the original number, and that when you have a number over itself, it equals 1. Get ready, get set...GO! Test Your Knowledge 1) 2) 3) 4) How many irrational numbers are there between 1 and 8? Fewer than 3 3 6 7 More than 7 Answers: B, J, D, E Answer Explanations: 1) For this problem, we must combine our like terms in order to eventually isolate $k$ (for more on this, check out our guide to ACT single variable equations). We know that, when adding fractions, we must give them the same denominator, so we can manipulateour fractions to have matching denominators and solvefrom there. Alternatively, we could again use decimal points instead of fractions. We will go through both ways here. Method 1Fractions We have ${1/3}k$ and ${1/4}k$ that we must add. They share a common multiple of 12, so let us convert them to fractions out of 12. $1/3$ = ${1(4)}/{3(4)}$ = $4/12$ $1/4$ = ${1(3)}/{4(3)}$ = $3/12$ Now that they have the same numerator, we can combine them to be: $4/12 + 3/12 = 7/12$ So our equation is: ${7/12}k = 1$ Now we must divide both sides by $7/12$, which means that we must inverse and multiply. $k = 1(12/7)$ $k = 12/7$ So our final answer is B. Method 2Decimals Instead of using and converting fractions, we also could have used decimals instead. $1/3$ = $0.333$ $1/4$ = $0.25$ Because they are decimals, we can simply add them together to be: $0.333k + 0.25k = 0.583k$ $0.58k = 1$ $k = 1/0.583$ $k = 1.715$ Now, simply convert the answer choices to decimals tofind one that matches. In this case answer choice A would be far too small, and answers D and E are whole numbers, so they can all be eliminated. Answer choice C would be $7/2 = 3.5$. This leaves us with answer choice B: $12/7 = 1.714$ So our final answer is, again, B. 2) This question specifically asks for a rational number answer, but it is a bit deceptive, as a quick glance shows us that all the answer choices are rational numbers. This means you can ignore this stipulation for the time being. Again, we can solve this problem in one of two waysvia fractions or via decimals. We will go through both methods. Method 1Fractions We are trying to find a rational fraction halfway between $1/5$ and $1/3$, so let us convert them into fractions with the same denominator. A common multiple of 3 and 5 is 15, so let us make that their new denominator. $1/5$ = ${1(3)}/{5(3)}$ = $3/15$ $1/3$ =${1(5)}/{3(5)}$ = $5/15$ Well the rational number exactly halfway between $3/15$ and $5/15$ is $4/15$. So our answer is J, $4/15$. Method 2Decimals Again, if fractions aren't your favorite, you can always feel free to use decimals. First, convert $1/5$ and $1/3$ into decimals. $1/5 = 0.2$ $1/3 = 0.333$ Now, find the decimal halfway between them: ${0.2 + 0.333}/2 = 0.2665$ (For more on this process, check out our guide to ACT mean, median, and mode) Now, let us find the answer choice that, when converted into a decimal, matches our answer. If you know your decimals, then you know that $1/2 = 0.5$ and $1/4 = 0.25$, so these can be eliminated. We are now left with $2/15$, $4/15$, and $8/15$. The smart thing to do here is to pick the middle value and then go up or down if the mid value is too small or too large. So if we test $4/15$, we get: $4/15 = 0.2666$ Success! We nailed it at the mid value, no need to try the others. Our final answer is, again, J. 3) Even though this problem may, at first glance, look like a fraction problem, it is a ratio problem. We can tell because the question specifically asks for the ratios of the boys' sandwich consumption. If you're not paying attention, you can easily make a mistake and treat the questionas a fraction problem when ratios are written using the "/" symbol. So we have Jerome, who eats half the sandwich and Kevin, who eats one third, and Seth, who eats the rest. Now we can do this problem several ways, but let us pick two of the most straightforwardratio and fraction manipulation or plugging in your own numbers (for more on this strategy, check out guide to plugging in numbers). Method 1Ratio and Fraction Manipulation Because we are not told the portion of the sandwichthat Seth ate, we must find it. Fractions represent pieces of the whole and the whole is 1 (because anything over itself = 1). So let us add our two fractions and subtract that sum from 1 to find Seth's share of the sandwich. $1/2 + 1/3$. First, we must convert these fractions to ones with a shared denominator. Both 2 and 3 are multiples of 6, so we will use 6 as our new denominator. $1/2$ = ${1(3)}/{2(3)}$ = $3/6$ $1/3$ =${1(2)}/{3(2)}$ = $2/6$ Now, let us add them together and subtract their sum from 1. $3/6 + 2/6 = 5/6$ $1 - 5/6 = 1/6$ So Seth ate $1/6$ of the sandwich. And because these fractions now all share a common denominator, we can simply compare their numerators to find their ratio of sandwich shares (remember, ratios compare parts to other parts). So the sandwich eating fractions are: $3/6, 2/6,$ and $1/6$ When we just look at the numerators,the ratio is: $3:2:1$ Our final answer is D, $3:2:1$. Method 2Plugging in Numbers Instead of working exclusively with fractions and ratios, let's try the problem again using wholenumbers. We know that Jerome ate $1/2$ and sandwich and Kevin ate $1/3$, so let's give the sandwich an actual length value that is a shared multiple of those two numbers (note: our sandwich length does not have to be a multiple of 2 and 3it can be anything we want. It simply makes our lives easier to use a common multiple, as that way we can work with integers.) So let us say that the sandwich is 12 feet long. If Jerome ate half of it, then he ate: $12/2 = 6$ feet of sandwich. If Kevin ate one third of it, then he ate: $12/3 = 4$ feet of sandwich. If we add them together, they ate: $6 + 4 = 10$ feet of sandwich. Which means that Seth ate: $12 - 10 = 2$ feet of sandwich. Now let us compare their shares of 6, 4, and 2. $6:4:2$ We know that ratios can be reduced if each of the values shares a common factor. In this case, they can all be divided by 2, so let us reduce the ratio. $6:4:2$ = $3:2:1$ Again, our final answer is D, $3:2:1$ 4) This question asks you to find the amount of irrational numbers between two realnumbers, and the simple answer is that there are infinitely many. (Note: there isalso an infinite amount of rational numbers between any two realnumbers as well!). Why is this true? Think of it this way: The square root of 1 is rational, because it equals 1, which can be written as $1/1$. But the square root of 1.01 is irrational. And so is the square root of 1.02, and the square root of 1.03....None of these numbers can be written as ${\an \integer}/{\an \integer}$ (which you can tell because their decimals continue without repeating), and yet they all sitbetween 1 and 8 on a number line. So our final answer is E, more than 7 (and,in fact, infinite). Hurray and huzzah, you did it! The Take-Aways Don’t let fractions, ratios, and/or rational numbers intimidate you. Once you’ve mastered the basics behind how they behave, you’ll be able to work your way through many of the toughest fraction and ratio problems the ACT can put in your way The biggest point to look out for, when dealing with fractions and ratios, is not to mix them up! Always pay strict attention to times when you are comparing pieces to pieces or pieces to the whole. Though it can be easy to make a mistake during the test, don’t let yourself lose a point due to careless error. What’s Next? For you, fractions are a breeze, ratios were a snap, and rationals?Forget about it! Luckily for you, there is plenty more to tackle before test day.We have guides aplenty for the many math topics covered on the ACT, including trigonometry, integers, andsolid geometry. Running out of time duringACT Math practice? Check out our article on how to finish your math section before it's pencil's down. Don't know what score to aim for? Make sure you have a good grasp of whatkind of score would best suit your goals and current skill level, and how to improve it from there. Trying to push your score to the top? Look to our guide on how to get a perfect score, written by a 36 ACT-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

A Game of Thrones Chapter Seventy

He strapped his roll to the saddle, his scarred fingers stiff and clumsy. â€Å"Ghost,† he called softly, â€Å"to me.† And the wolf was there, eyes like embers. â€Å"Jon, please. You must not do this.† He mounted, the reins in his hand, and wheeled the horse around to face the night. Samwell Tarly stood in the stable door, a full moon peering over his shoulder. He threw a giant’s shadow, immense and black. â€Å"Get out of my way, Sam.† â€Å"Jon, you can’t,† Sam said. â€Å"I won’t let you.† â€Å"I would sooner not hurt you,† Jon told him. â€Å"Move aside, Sam, or I’ll ride you down.† â€Å"You won’t. You have to listen to me. Please . . . â€Å" Jon put his spurs to horseflesh, and the mare bolted for the door. For an instant Sam stood his ground, his face as round and pale as the moon behind him, his mouth a widening O of surprise. At the last moment, when they were almost on him, he jumped aside as Jon had known he would, stumbled, and fell. The mare leapt over him, out into the night. Jon raised the hood of his heavy cloak and gave the horse her head. Castle Black was silent and still as he rode out, with Ghost racing at his side. Men watched from the Wall behind him, he knew, but their eyes were turned north, not south. No one would see him go, no one but Sam Tarly, struggling back to his feet in the dust of the old stables. He hoped Sam hadn’t hurt himself, falling like that. He was so heavy and so ungainly, it would be just like him to break a wrist or twist his ankle getting out of the way. â€Å"I warned him,† Jon said aloud. â€Å"It was nothing to do with him, anyway.† He flexed his burned hand as he rode, opening and closing the scarred fingers. They still pained him, but it felt good to have the wrappings off. Moonlight silvered the hills as he followed the twisting ribbon of the kingsroad. He needed to get as far from the Wall as he could before they realized he was gone. On the morrow he would leave the road and strike out overland through field and bush and stream to throw off pursuit, but for the moment speed was more important than deception. It was not as though they would not guess where he was going. The Old Bear was accustomed to rise at first light, so Jon had until dawn to put as many leagues as he could between him and the Wall . . . if Sam Tarly did not betray him. The fat boy was dutiful and easily frightened, but he loved Jon like a brother. If questioned, Sam would doubtless tell them the truth, but Jon could not imagine him braving the guards in front of the King’s Tower to wake Mormont from sleep. When Jon did not appear to fetch the Old Bear’s breakfast from the kitchen, they’d look in his cell and find Longclaw on the bed. It had been hard to abandon it, but Jon was not so lost to honor as to take it with him. Even Jorah Mormont had not done that, when he fled in disgrace. Doubtless Lord Mormont would find someone more worthy of the blade. Jon felt bad when he thought of the old man. He knew his desertion would be salt in the still-raw wound of his son’s disgrace. That seemed a poor way to repay him for his trust, but it couldn’t be helped. No matter what he did, Jon felt as though he were betraying someone. Even now, he did not know if he was doing the honorable thing. The southron had it easier. They had their septons to talk to, someone to tell them the gods’ will and help sort out right from wrong. But the Starks worshiped the old gods, the nameless gods, and if the heart trees heard, they did not speak. When the last lights of Castle Black vanished behind him, Jon slowed his mare to a walk. He had a long journey ahead and only the one horse to see him through. There were holdfasts and farming villages along the road south where he might be able to trade the mare for a fresh mount when he needed one, but not if she were injured or blown. He would need to find new clothes soon; most like, he’d need to steal them. He was clad in black from head to heel; high leather riding boots, roughspun breeches and tunic, sleeveless leather jerkin, and heavy wool cloak. His longsword and dagger were sheathed in black moleskin, and the hauberk and coif in his saddlebag were black ringmail. Any bit of it could mean his death if he were taken. A stranger wearing black was viewed with cold suspicion in every village and holdfast north of the Neck, and men would soon be watching for him. Once Maester Aemon’s ravens took flight, Jon knew he would find no safe haven. Not even at Winterfell. Bran might want to let him in, but Maester Luwin had better sense. He would bar the gates and send Jon away, as he should. Better not to call there at all. Yet he saw the castle clear in his mind’s eye, as if he had left it only yesterday; the towering granite walls, the Great Hall with its smells of smoke and dog and roasting meat, his father’s solar, the turret room where he had slept. Part of him wanted nothing so much as to hear Bran laugh again, to sup on one of Gage’s beef-and-bacon pies, to listen to Old Nan tell her tales of the children of the forest and Florian the Fool. But he had not left the Wall for that; he had left because he was after all his father’s son, and Robb’s brother. The gift of a sword, even a sword as fine as Longclaw, did not make him a Mormont. Nor was he Aemon Targaryen. Three times the old man had chosen, and three times he had chosen honor, but that was him. Even now, Jon could not decide whether the maester had stayed because he was weak and craven, or because he was strong and true. Yet he understood what the old man had meant, about the pain of choosing; he understood that all too well. Tyrion Lannister had claimed that most men would rather deny a hard truth than face it, but Jon was done with denials. He was who he was; Jon Snow, bastard and oathbreaker, motherless, friendless, and damned. For the rest of his life—however long that might be—he would be condemned to be an outsider, the silent man standing in the shadows who dares not speak his true name. Wherever he might go throughout the Seven Kingdoms, he would need to live a lie, lest every man’s hand be raised against him. But it made no matter, so long as he lived long enough to take his place by his brother’s side and help avenge his father. He remembered Robb as he had last seen him, standing in the yard with snow melting in his auburn hair. Jon would have to come to him in secret, disguised. He tried to imagine the look on Robb’s face when he revealed himself. His brother would shake his head and smile, and he’d say . . . he’d say . . . He could not see the smile. Hard as he tried, he could not see it. He found himself thinking of the deserter his father had beheaded the day they’d found the direwolves. â€Å"You said the words,† Lord Eddard had told him. â€Å"You took a vow, before your brothers, before the old gods and the new.† Desmond and Fat Tom had dragged the man to the stump. Bran’s eyes had been wide as saucers, and Jon had to remind him to keep his pony in hand. He remembered the look on Father’s face when Theon Greyjoy brought forth Ice, the spray of blood on the snow, the way Theon had kicked the head when it came rolling at his feet. He wondered what Lord Eddard might have done if the deserter had been his brother Benjen instead of that ragged stranger. Would it have been any different? It must, surely, surely . . . and Robb would welcome him, for a certainty. He had to, or else . . . It did not bear thinking about. Pain throbbed, deep in his fingers, as he clutched the reins. Jon put his heels into his horse and broke into a gallop, racing down the kingsroad, as if to outrun his doubts. Jon was not afraid of death, but he did not want to die like that, trussed and bound and beheaded like a common brigand. If he must perish, let it be with a sword in his hand, fighting his father’s killers. He was no true Stark, had never been one . . . but he could die like one. Let them say that Eddard Stark had fathered four sons, not three. Ghost kept pace with them for almost half a mile, red tongue lolling from his mouth. Man and horse alike lowered their heads as he asked the mare for more speed. The wolf slowed, stopped, watching, his eyes glowing red in the moonlight. He vanished behind, but Jon knew he would follow, at his own pace. Scattered lights flickered through the trees ahead of him, on both sides of the road: Mole’s Town. A dog barked as he rode through, and he heard a mule’s raucous haw from the stable, but otherwise the village was still. Here and there the glow of hearth fires shone through shuttered windows, leaking between wooden slats, but only a few. Mole’s Town was bigger than it seemed, but three quarters of it was under the ground, in deep warm cellars connected by a maze of tunnels. Even the whorehouse was down there, nothing on the surface but a wooden shack no bigger than a privy, with a red lantern hung over the door. On the Wall, he’d heard men call the whores â€Å"buried treasures.† He wondered whether any of his brothers in black were down there tonight, mining. That was oathbreaking too, yet no one seemed to care. Not until he was well beyond the village did Jon slow again. By then both he and the mare were damp with sweat. He dismounted, shivering, his burned hand aching. A bank of melting snow lay under the trees, bright in the moonlight, water trickling off to form small shallow pools. Jon squatted and brought his hands together, cupping the runoff between his fingers. The snowmelt was icy cold. He drank, and splashed some on his face, until his cheeks tingled. His fingers were throbbing worse than they had in days, and his head was pounding too. I am doing the right thing, he told himself, so why do I feel so bad? The horse was well lathered, so Jon took the lead and walked her for a while. The road was scarcely wide enough for two riders to pass abreast, its surface cut by tiny streams and littered with stone. That run had been truly stupid, an invitation to a broken neck. Jon wondered what had gotten into him. Was he in such a great rush to die? Off in the trees, the distant scream of some frightened animal made him look up. His mare whinnied nervously. Had his wolf found some prey? He cupped his hands around his mouth. â€Å"Ghost!† he shouted. â€Å"Ghost, to me.† The only answer was a rush of wings behind him as an owl took flight. Frowning, Jon continued on his way. He led the mare for half an hour, until she was dry. Ghost did not appear. Jon wanted to mount up and ride again, but he was concerned about his missing wolf. â€Å"Ghost,† he called again. â€Å"Where are you? To me! Ghost!† Nothing in these woods could trouble a direwolf, even a half-grown direwolf, unless . . . no, Ghost was too smart to attack a bear, and if there was a wolf pack anywhere close Jon would have surely heard them howling. He should eat, he decided. Food would settle his stomach and give Ghost the chance to catch up. There was no danger yet; Castle Black still slept. In his saddlebag, he found a biscuit, a piece of cheese, and a small withered brown apple. He’d brought salt beef as well, and a rasher of bacon he’d filched from the kitchens, but he would save the meat for the morrow. After it was gone he’d need to hunt, and that would slow him. Jon sat under the trees and ate his biscuit and cheese while his mare grazed along the kingsroad. He kept the apple for last. It had gone a little soft, but the flesh was still tart and juicy. He was down to the core when he heard the sounds: horses, and from the north. Quickly Jon leapt up and strode to his mare. Could he outrun them? No, they were too close, they’d hear him for a certainty, and if they were from Castle Black . . . He led the mare off the road, behind a thick stand of grey-green sentinels. â€Å"Ouiet now,† he said in a hushed voice, crouching down to peer through the branches. If the gods were kind, the riders would pass by. Likely as not, they were only smallfolk from Mole’s Town, farmers on their way to their fields, although what they were doing out in the middle of the night . . . He listened to the sound of hooves growing steadily louder as they trotted briskly down the kingsroad. From the sound, there were five or six of them at the least. Their voices drifted through the trees. † . . . certain he came this way?† â€Å"We can’t be certain.† â€Å"He could have ridden east, for all you know. Or left the road to cut through the woods. That’s what I’d do.† â€Å"In the dark? Stupid. If you didn’t fall off your horse and break your neck, you’d get lost and wind up back at the Wall when the sun came up.† â€Å"I would not.† Grenn sounded peeved. â€Å"I’d just ride south, you can tell south by the stars.† â€Å"What if the sky was cloudy?† Pyp asked. â€Å"Then I wouldn’t go.† Another voice broke in. â€Å"You know where I’d be if it was me? I’d be in Mole’s Town, digging for buried treasure.† Toad’s shrill laughter boomed through the trees. Jon’s mare snorted. â€Å"Keep quiet, all of you,† Haider said. â€Å"I thought I heard something.† â€Å"Where? I didn’t hear anything.† The horses stopped. â€Å"You can’t hear yourself fart.† â€Å"I can too,† Grenn insisted. â€Å"Quiet!† They all fell silent, listening. Jon found himself holding his breath. Sam, he thought. He hadn’t gone to the Old Bear, but he hadn’t gone to bed either, he’d woken the other boys. Damn them all. Come dawn, if they were not in their beds, they’d be named deserters too. What did they think they were doing? The hushed silence seemed to stretch on and on. From where Jon crouched, he could see the legs of their horses through the branches. Finally Pyp spoke up. â€Å"What did you hear?† â€Å"I don’t know,† Haider admitted. â€Å"A sound, I thought it might have been a horse but . . . â€Å" â€Å"There’s nothing here.† Out of the corner of his eye, Jon glimpsed a pale shape moving through the trees. Leaves rustled, and Ghost came bounding out of the shadows, so suddenly that Jon’s mare started and gave a whinny. â€Å"There!† Halder shouted. â€Å"I heard it too!† â€Å"Traitor,† Jon told the direwolf as he swung up into the saddle. He turned the mare’s head to slide off through the trees, but they were on him before he had gone ten feet. â€Å"Jon!† Pyp shouted after him. â€Å"Pull up,† Grenn said. â€Å"You can’t outrun us all.† Jon wheeled around to face them, drawing his sword. â€Å"Get back. I don’t wish to hurt you, but I will if I have to.† â€Å"One against seven?† Halder gave a signal. The boys spread out, surrounding him. â€Å"What do you want with me?† Jon demanded. â€Å"We want to take you back where you belong,† Pyp said. â€Å"I belong with my brother.† â€Å"We’re your brothers now,† Grenn said. â€Å"They’ll cut off your head if they catch you, you know,† Toad put in with a nervous laugh. â€Å"This is so stupid, it’s like something the Aurochs would do.† â€Å"I would not,† Grenn said. â€Å"I’m no oathbreaker. I said the words and I meant them.† â€Å"So did I,† Jon told them. â€Å"Don’t you understand? They murdered my father. It’s war, my brother Robb is fighting in the riverlands—† â€Å"We know,† said Pyp solemnly. â€Å"Sam told us everything.† â€Å"We’re sorry about your father,† Grenn said, â€Å"but it doesn’t matter. Once you say the words, you can’t leave, no matter what.† â€Å"I have to,† Jon said fervently. â€Å"You said the words,† Pyp reminded him. â€Å"Now my watch begins, you said it. It shall not end until my death.† â€Å"I shall live and die at my post,† Grenn added, nodding. â€Å"You don’t have to tell me the words, I know them as well as you do.† He was angry now. Why couldn’t they let him go in peace? They were only making it harder. â€Å"I am the sword in the darkness,† Halder intoned. â€Å"The watcher on the walls,† piped Toad. Jon cursed them all to their faces. They took no notice. Pyp spurred his horse closer, reciting, â€Å"I am the fire that burns against the cold, the light that brings the dawn, the horn that wakes the sleepers, the shield that guards the realms of men.† â€Å"Stay back,† Jon warned him, brandishing his sword. â€Å"I mean it, Pyp.† They weren’t even wearing armor, he could cut them to pieces if he had to. Matthar had circled behind him. He joined the chorus. â€Å"I pledge my life and honor to the Night’s Watch.† Jon kicked his mare, spinning her in a circle. The boys were all around him now, closing from every side. â€Å"For this night . . . † Halder trotted in from the left. † . . . and all the nights to come,† finished Pyp. He reached over for Jon’s reins. â€Å"So here are your choices. Kill me, or come back with me.† Jon lifted his sword . . . and lowered it, helpless. â€Å"Damn you,† he said. â€Å"Damn you all.† â€Å"Do we have to bind your hands, or will you give us your word you’ll ride back peaceful?† asked Halder. â€Å"I won’t run, if that’s what you mean.† Ghost moved out from under the trees and Jon glared at him. â€Å"Small help you were,† he said. The deep red eyes looked at him knowingly. â€Å"We had best hurry,† Pyp said. â€Å"If we’re not back before first light, the Old Bear will have all our heads.† Of the ride back, Jon Snow remembered little. It seemed shorter than the journey south, perhaps because his mind was elsewhere. Pyp set the pace, galloping, walking, trotting, and then breaking into another gallop. Mole’s Town came and went, the red lantern over the brothel long extinguished. They made good time. Dawn was still an hour off when Jon glimpsed the towers of Castle Black ahead of them, dark against the pale immensity of the Wall. It did not seem like home this time. They could take him back, Jon told himself, but they could not make him stay. The war would not end on the morrow, or the day after, and his friends could not watch him day and night. He would bide his time, make them think he was content to remain here . . . and then, when they had grown lax, he would be off again. Next time he would avoid the kingsroad. He could follow the Wall east, perhaps all the way to the sea, a longer route but a safer one. Or even west, to the mountains, and then south over the high passes. That was the wildling’s way, hard and perilous, but at least no one wouid follow him. He wouldn’t stray within a hundred leagues of Winterfell or the kingsroad. Samwell Tarly awaited them in the old stables, slumped on the ground against a bale of hay, too anxious to sleep. He rose and brushed himself off. â€Å"I . . . I’m glad they found you, Jon.† â€Å"I’m not,† Jon said, dismounting. Pyp hopped off his horse and looked at the lightening sky with disgust. â€Å"Give us a hand bedding down the horses, Sam,† the small boy said. â€Å"We have a long day before us, and no sleep to face it on, thanks to Lord Snow.† When day broke, Jon walked to the kitchens as he did every dawn. Three-Finger Hobb said nothing as he gave him the Old Bear’s breakfast. Today it was three brown eggs boiled hard, with fried bread and ham steak and a bowl of wrinkled plums. Jon carried the food back to the King’s Tower. He found Mormont at the window seat, writing. His raven was walking back and forth across his shoulders, muttering, â€Å"Corn, corn, corn.† The bird shrieked when Jon entered. â€Å"Put the food on the table,† the Old Bear said, glancing up. â€Å"I’ll have some beer.† Jon opened a shuttered window, took the flagon of beer off the outside ledge, and filled a horn. Hobb had given him a lemon, still cold from the Wall. Jon crushed it in his fist. The juice trickled through his fingers. Mormont drank lemon in his beer every day, and claimed that was why he still had his own teeth. â€Å"Doubtless you loved your father,† Mormont said when Jon brought him his horn. â€Å"The things we love destroy us every time, lad. Remember when I told you that?† â€Å"I remember,† Jon said sullenly. He did not care to talk of his father’s death, not even to Mormont. â€Å"See that you never forget it. The hard truths are the ones to hold tight. Fetch me my plate. Is it ham again? So be it. You look weary. Was your moonlight ride so tiring?† Jon’s throat was dry. â€Å"You know?† â€Å"Know,† the raven echoed from Mormont’s shoulder. â€Å"Know.† The Old Bear snorted. â€Å"Do you think they chose me Lord Commander of the Night’s Watch because I’m dumb as a stump, Snow? Aemon told me you’d go. I told him you’d be back. I know my men . . . and my boys too. Honor set you on the kingsroad . . . and honor brought you back.† â€Å"My friends brought me back,† Jon said. â€Å"Did I say it was your honor?† Mormont inspected his plate. â€Å"They killed my father. Did you expect me to do nothing?† â€Å"If truth be told, we expected you to do just as you did.† Mormont tried a plum, spit out the pit. â€Å"I ordered a watch kept over you., You were seen leaving. If your brothers had not fetched you back, you would have been taken along the way, and not by friends. Unless you have a horse with wings like a raven. Do you?† â€Å"No.† Jon felt like a fool. â€Å"Pity, we could use a horse like that.† Jon stood tall. He told himself that he would die well; that much he could do, at the least. â€Å"I know the penalty for desertion, my lord. I’m not afraid to die.† â€Å"Die!† the raven cried. â€Å"Nor live, I hope,† Mormont said, cutting his ham with a dagger and feeding a bite to the bird. â€Å"You have not deserted—yet. Here you stand. If we beheaded every boy who rode to Mole’s Town in the night, only ghosts would guard the Wall. Yet maybe you mean to flee again on the morrow, or a fortnight from now. Is that it? Is that your hope, boy?† Jon kept silent. â€Å"I thought so.† Mormont peeled the shell off a boiled egg. â€Å"Your father is dead, lad. Do you think you can bring him back?† â€Å"No,† he answered, sullen. â€Å"Good,† Mormont said. â€Å"We’ve seen the dead come back, you and me, and it’s not something I care to see again.† He ate the egg in two bites and flicked a bit of shell out from between his teeth. â€Å"Your brother is in the field with all the power of the north behind him. Any one of his lords bannermen commands more swords than you’ll find in all the Night’s Watch. Why do you imagine that they need your help? Are you such a mighty warrior, or do you carry a grumkin in your pocket to magic up your sword?† Jon had no answer for him. The raven was pecking at an egg, breaking the shell. Pushing his beak through the hole, he pulled out morsels of white and yoke. The Old Bear sighed. â€Å"You are not the only one touched by this war. Like as not, my sister is marching in your brother’s host, her and those daughters of hers, dressed in men’s mail. Maege is a hoary old snark, stubborn, short-tempered, and willful. Truth be told, I can hardly stand to be around the wretched woman, but that does not mean my love for her is any less than the love you bear your half sisters.† Frowning, Mormont took his last egg and squeezed it in his fist until the shell crunched. â€Å"Or perhaps it does. Be that as it may, I’d still grieve if she were slain, yet you don’t see me running off. I said the words, just as you did. My place is here . . . where is yours, boy?† I have no place, Jon wanted to say, I’m a bastard, I have no rights, no name, no mother, and now not even a father. The words would not come. â€Å"I don’t know.† â€Å"I do,† said Lord Commander Mormont. â€Å"The cold winds are rising, Snow. Beyond the Wall, the shadows lengthen. Cotter Pyke writes of vast herds of elk, streaming south and east toward the sea, and mammoths as well. He says one of his men discovered huge, misshapen footprints not three leagues from Eastwatch. Rangers from the Shadow Tower have found whole villages abandoned, and at night Ser Denys says they see fires in the mountains, huge blazes that burn from dusk till dawn. Quorin Halfhand took a captive in the depths of the Gorge, and the man swears that Mance Rayder is massing all his people in some new, secret stronghold he’s found, to what end the gods only know. Do you think your uncle Benjen was the only ranger we’ve lost this past year?† â€Å"Ben Jen,† the raven squawked, bobbing its head, bits of egg dribbling from its beak. â€Å"Ben Jen. Ben Jen.† â€Å"No,† Jon said. There had been others. Too many. â€Å"Do you think your brother’s war is more important than ours?† the old man barked. Jon chewed his lip. The raven flapped its wings at him. â€Å"War, war, war, war,† it sang. â€Å"It’s not,† Mormont told him. â€Å"Gods save us, boy, you’re not blind and you’re not stupid. When dead men come hunting in the night, do you think it matters who sits the Iron Throne?† â€Å"No.† Jon had not thought of it that way. â€Å"Your lord father sent you to us, Jon. Why, who can say?† â€Å"Why? Why? Why?† the raven called. â€Å"All I know is that the blood of the First Men flows in the veins of the Starks. The First Men built the Wall, and it’s said they remember things otherwise forgotten. And that beast of yours . . . he led us to the wights, warned you of the dead man on the steps. Ser Jaremy would doubtless call that happenstance, yet Ser Jaremy is dead and I’m not.† Lord Mormont stabbed a chunk of ham with the point of his dagger. â€Å"I think you were meant to be here, and I want you and that wolf of yours with us when we go beyond the Wall.† His words sent a chill of excitement down Jon’s back. â€Å"Beyond the Wall?† â€Å"You heard me. I mean to find Ben Stark, alive or dead.† He chewed and swallowed. â€Å"I will not sit here meekly and wait for the snows and the ice winds. We must know what is happening. This time the Night’s Watch will ride in force, against the King-beyond-the-Wall, the Others, and anything else that may be out there. I mean to command them myself.† He pointed his dagger at Jon’s chest. â€Å"By custom, the Lord Commander’s steward is his squire as well . . . but I do not care to wake every dawn wondering if you’ve run off again. So I will have an answer from you, Lord Snow, and I will have it now. Are you a brother of the Night’s Watch . . . or only a bastard boy who wants to play at war?† Jon Snow straightened himself and took a long deep breath. Forgive me, Father. Robb, Arya, Bran . . . forgive me, I cannot help you. He has the truth of it. This is my place. â€Å"I am . . . yours, my lord. Your man. I swear it. I will not run again.† The Old Bear snorted. â€Å"Good. Now go put on your sword.† A Game of Thrones Chapter Seventy He strapped his roll to the saddle, his scarred fingers stiff and clumsy. â€Å"Ghost,† he called softly, â€Å"to me.† And the wolf was there, eyes like embers. â€Å"Jon, please. You must not do this.† He mounted, the reins in his hand, and wheeled the horse around to face the night. Samwell Tarly stood in the stable door, a full moon peering over his shoulder. He threw a giant’s shadow, immense and black. â€Å"Get out of my way, Sam.† â€Å"Jon, you can’t,† Sam said. â€Å"I won’t let you.† â€Å"I would sooner not hurt you,† Jon told him. â€Å"Move aside, Sam, or I’ll ride you down.† â€Å"You won’t. You have to listen to me. Please . . . â€Å" Jon put his spurs to horseflesh, and the mare bolted for the door. For an instant Sam stood his ground, his face as round and pale as the moon behind him, his mouth a widening O of surprise. At the last moment, when they were almost on him, he jumped aside as Jon had known he would, stumbled, and fell. The mare leapt over him, out into the night. Jon raised the hood of his heavy cloak and gave the horse her head. Castle Black was silent and still as he rode out, with Ghost racing at his side. Men watched from the Wall behind him, he knew, but their eyes were turned north, not south. No one would see him go, no one but Sam Tarly, struggling back to his feet in the dust of the old stables. He hoped Sam hadn’t hurt himself, falling like that. He was so heavy and so ungainly, it would be just like him to break a wrist or twist his ankle getting out of the way. â€Å"I warned him,† Jon said aloud. â€Å"It was nothing to do with him, anyway.† He flexed his burned hand as he rode, opening and closing the scarred fingers. They still pained him, but it felt good to have the wrappings off. Moonlight silvered the hills as he followed the twisting ribbon of the kingsroad. He needed to get as far from the Wall as he could before they realized he was gone. On the morrow he would leave the road and strike out overland through field and bush and stream to throw off pursuit, but for the moment speed was more important than deception. It was not as though they would not guess where he was going. The Old Bear was accustomed to rise at first light, so Jon had until dawn to put as many leagues as he could between him and the Wall . . . if Sam Tarly did not betray him. The fat boy was dutiful and easily frightened, but he loved Jon like a brother. If questioned, Sam would doubtless tell them the truth, but Jon could not imagine him braving the guards in front of the King’s Tower to wake Mormont from sleep. When Jon did not appear to fetch the Old Bear’s breakfast from the kitchen, they’d look in his cell and find Longclaw on the bed. It had been hard to abandon it, but Jon was not so lost to honor as to take it with him. Even Jorah Mormont had not done that, when he fled in disgrace. Doubtless Lord Mormont would find someone more worthy of the blade. Jon felt bad when he thought of the old man. He knew his desertion would be salt in the still-raw wound of his son’s disgrace. That seemed a poor way to repay him for his trust, but it couldn’t be helped. No matter what he did, Jon felt as though he were betraying someone. Even now, he did not know if he was doing the honorable thing. The southron had it easier. They had their septons to talk to, someone to tell them the gods’ will and help sort out right from wrong. But the Starks worshiped the old gods, the nameless gods, and if the heart trees heard, they did not speak. When the last lights of Castle Black vanished behind him, Jon slowed his mare to a walk. He had a long journey ahead and only the one horse to see him through. There were holdfasts and farming villages along the road south where he might be able to trade the mare for a fresh mount when he needed one, but not if she were injured or blown. He would need to find new clothes soon; most like, he’d need to steal them. He was clad in black from head to heel; high leather riding boots, roughspun breeches and tunic, sleeveless leather jerkin, and heavy wool cloak. His longsword and dagger were sheathed in black moleskin, and the hauberk and coif in his saddlebag were black ringmail. Any bit of it could mean his death if he were taken. A stranger wearing black was viewed with cold suspicion in every village and holdfast north of the Neck, and men would soon be watching for him. Once Maester Aemon’s ravens took flight, Jon knew he would find no safe haven. Not even at Winterfell. Bran might want to let him in, but Maester Luwin had better sense. He would bar the gates and send Jon away, as he should. Better not to call there at all. Yet he saw the castle clear in his mind’s eye, as if he had left it only yesterday; the towering granite walls, the Great Hall with its smells of smoke and dog and roasting meat, his father’s solar, the turret room where he had slept. Part of him wanted nothing so much as to hear Bran laugh again, to sup on one of Gage’s beef-and-bacon pies, to listen to Old Nan tell her tales of the children of the forest and Florian the Fool. But he had not left the Wall for that; he had left because he was after all his father’s son, and Robb’s brother. The gift of a sword, even a sword as fine as Longclaw, did not make him a Mormont. Nor was he Aemon Targaryen. Three times the old man had chosen, and three times he had chosen honor, but that was him. Even now, Jon could not decide whether the maester had stayed because he was weak and craven, or because he was strong and true. Yet he understood what the old man had meant, about the pain of choosing; he understood that all too well. Tyrion Lannister had claimed that most men would rather deny a hard truth than face it, but Jon was done with denials. He was who he was; Jon Snow, bastard and oathbreaker, motherless, friendless, and damned. For the rest of his life—however long that might be—he would be condemned to be an outsider, the silent man standing in the shadows who dares not speak his true name. Wherever he might go throughout the Seven Kingdoms, he would need to live a lie, lest every man’s hand be raised against him. But it made no matter, so long as he lived long enough to take his place by his brother’s side and help avenge his father. He remembered Robb as he had last seen him, standing in the yard with snow melting in his auburn hair. Jon would have to come to him in secret, disguised. He tried to imagine the look on Robb’s face when he revealed himself. His brother would shake his head and smile, and he’d say . . . he’d say . . . He could not see the smile. Hard as he tried, he could not see it. He found himself thinking of the deserter his father had beheaded the day they’d found the direwolves. â€Å"You said the words,† Lord Eddard had told him. â€Å"You took a vow, before your brothers, before the old gods and the new.† Desmond and Fat Tom had dragged the man to the stump. Bran’s eyes had been wide as saucers, and Jon had to remind him to keep his pony in hand. He remembered the look on Father’s face when Theon Greyjoy brought forth Ice, the spray of blood on the snow, the way Theon had kicked the head when it came rolling at his feet. He wondered what Lord Eddard might have done if the deserter had been his brother Benjen instead of that ragged stranger. Would it have been any different? It must, surely, surely . . . and Robb would welcome him, for a certainty. He had to, or else . . . It did not bear thinking about. Pain throbbed, deep in his fingers, as he clutched the reins. Jon put his heels into his horse and broke into a gallop, racing down the kingsroad, as if to outrun his doubts. Jon was not afraid of death, but he did not want to die like that, trussed and bound and beheaded like a common brigand. If he must perish, let it be with a sword in his hand, fighting his father’s killers. He was no true Stark, had never been one . . . but he could die like one. Let them say that Eddard Stark had fathered four sons, not three. Ghost kept pace with them for almost half a mile, red tongue lolling from his mouth. Man and horse alike lowered their heads as he asked the mare for more speed. The wolf slowed, stopped, watching, his eyes glowing red in the moonlight. He vanished behind, but Jon knew he would follow, at his own pace. Scattered lights flickered through the trees ahead of him, on both sides of the road: Mole’s Town. A dog barked as he rode through, and he heard a mule’s raucous haw from the stable, but otherwise the village was still. Here and there the glow of hearth fires shone through shuttered windows, leaking between wooden slats, but only a few. Mole’s Town was bigger than it seemed, but three quarters of it was under the ground, in deep warm cellars connected by a maze of tunnels. Even the whorehouse was down there, nothing on the surface but a wooden shack no bigger than a privy, with a red lantern hung over the door. On the Wall, he’d heard men call the whores â€Å"buried treasures.† He wondered whether any of his brothers in black were down there tonight, mining. That was oathbreaking too, yet no one seemed to care. Not until he was well beyond the village did Jon slow again. By then both he and the mare were damp with sweat. He dismounted, shivering, his burned hand aching. A bank of melting snow lay under the trees, bright in the moonlight, water trickling off to form small shallow pools. Jon squatted and brought his hands together, cupping the runoff between his fingers. The snowmelt was icy cold. He drank, and splashed some on his face, until his cheeks tingled. His fingers were throbbing worse than they had in days, and his head was pounding too. I am doing the right thing, he told himself, so why do I feel so bad? The horse was well lathered, so Jon took the lead and walked her for a while. The road was scarcely wide enough for two riders to pass abreast, its surface cut by tiny streams and littered with stone. That run had been truly stupid, an invitation to a broken neck. Jon wondered what had gotten into him. Was he in such a great rush to die? Off in the trees, the distant scream of some frightened animal made him look up. His mare whinnied nervously. Had his wolf found some prey? He cupped his hands around his mouth. â€Å"Ghost!† he shouted. â€Å"Ghost, to me.† The only answer was a rush of wings behind him as an owl took flight. Frowning, Jon continued on his way. He led the mare for half an hour, until she was dry. Ghost did not appear. Jon wanted to mount up and ride again, but he was concerned about his missing wolf. â€Å"Ghost,† he called again. â€Å"Where are you? To me! Ghost!† Nothing in these woods could trouble a direwolf, even a half-grown direwolf, unless . . . no, Ghost was too smart to attack a bear, and if there was a wolf pack anywhere close Jon would have surely heard them howling. He should eat, he decided. Food would settle his stomach and give Ghost the chance to catch up. There was no danger yet; Castle Black still slept. In his saddlebag, he found a biscuit, a piece of cheese, and a small withered brown apple. He’d brought salt beef as well, and a rasher of bacon he’d filched from the kitchens, but he would save the meat for the morrow. After it was gone he’d need to hunt, and that would slow him. Jon sat under the trees and ate his biscuit and cheese while his mare grazed along the kingsroad. He kept the apple for last. It had gone a little soft, but the flesh was still tart and juicy. He was down to the core when he heard the sounds: horses, and from the north. Quickly Jon leapt up and strode to his mare. Could he outrun them? No, they were too close, they’d hear him for a certainty, and if they were from Castle Black . . . He led the mare off the road, behind a thick stand of grey-green sentinels. â€Å"Ouiet now,† he said in a hushed voice, crouching down to peer through the branches. If the gods were kind, the riders would pass by. Likely as not, they were only smallfolk from Mole’s Town, farmers on their way to their fields, although what they were doing out in the middle of the night . . . He listened to the sound of hooves growing steadily louder as they trotted briskly down the kingsroad. From the sound, there were five or six of them at the least. Their voices drifted through the trees. † . . . certain he came this way?† â€Å"We can’t be certain.† â€Å"He could have ridden east, for all you know. Or left the road to cut through the woods. That’s what I’d do.† â€Å"In the dark? Stupid. If you didn’t fall off your horse and break your neck, you’d get lost and wind up back at the Wall when the sun came up.† â€Å"I would not.† Grenn sounded peeved. â€Å"I’d just ride south, you can tell south by the stars.† â€Å"What if the sky was cloudy?† Pyp asked. â€Å"Then I wouldn’t go.† Another voice broke in. â€Å"You know where I’d be if it was me? I’d be in Mole’s Town, digging for buried treasure.† Toad’s shrill laughter boomed through the trees. Jon’s mare snorted. â€Å"Keep quiet, all of you,† Haider said. â€Å"I thought I heard something.† â€Å"Where? I didn’t hear anything.† The horses stopped. â€Å"You can’t hear yourself fart.† â€Å"I can too,† Grenn insisted. â€Å"Quiet!† They all fell silent, listening. Jon found himself holding his breath. Sam, he thought. He hadn’t gone to the Old Bear, but he hadn’t gone to bed either, he’d woken the other boys. Damn them all. Come dawn, if they were not in their beds, they’d be named deserters too. What did they think they were doing? The hushed silence seemed to stretch on and on. From where Jon crouched, he could see the legs of their horses through the branches. Finally Pyp spoke up. â€Å"What did you hear?† â€Å"I don’t know,† Haider admitted. â€Å"A sound, I thought it might have been a horse but . . . â€Å" â€Å"There’s nothing here.† Out of the corner of his eye, Jon glimpsed a pale shape moving through the trees. Leaves rustled, and Ghost came bounding out of the shadows, so suddenly that Jon’s mare started and gave a whinny. â€Å"There!† Halder shouted. â€Å"I heard it too!† â€Å"Traitor,† Jon told the direwolf as he swung up into the saddle. He turned the mare’s head to slide off through the trees, but they were on him before he had gone ten feet. â€Å"Jon!† Pyp shouted after him. â€Å"Pull up,† Grenn said. â€Å"You can’t outrun us all.† Jon wheeled around to face them, drawing his sword. â€Å"Get back. I don’t wish to hurt you, but I will if I have to.† â€Å"One against seven?† Halder gave a signal. The boys spread out, surrounding him. â€Å"What do you want with me?† Jon demanded. â€Å"We want to take you back where you belong,† Pyp said. â€Å"I belong with my brother.† â€Å"We’re your brothers now,† Grenn said. â€Å"They’ll cut off your head if they catch you, you know,† Toad put in with a nervous laugh. â€Å"This is so stupid, it’s like something the Aurochs would do.† â€Å"I would not,† Grenn said. â€Å"I’m no oathbreaker. I said the words and I meant them.† â€Å"So did I,† Jon told them. â€Å"Don’t you understand? They murdered my father. It’s war, my brother Robb is fighting in the riverlands—† â€Å"We know,† said Pyp solemnly. â€Å"Sam told us everything.† â€Å"We’re sorry about your father,† Grenn said, â€Å"but it doesn’t matter. Once you say the words, you can’t leave, no matter what.† â€Å"I have to,† Jon said fervently. â€Å"You said the words,† Pyp reminded him. â€Å"Now my watch begins, you said it. It shall not end until my death.† â€Å"I shall live and die at my post,† Grenn added, nodding. â€Å"You don’t have to tell me the words, I know them as well as you do.† He was angry now. Why couldn’t they let him go in peace? They were only making it harder. â€Å"I am the sword in the darkness,† Halder intoned. â€Å"The watcher on the walls,† piped Toad. Jon cursed them all to their faces. They took no notice. Pyp spurred his horse closer, reciting, â€Å"I am the fire that burns against the cold, the light that brings the dawn, the horn that wakes the sleepers, the shield that guards the realms of men.† â€Å"Stay back,† Jon warned him, brandishing his sword. â€Å"I mean it, Pyp.† They weren’t even wearing armor, he could cut them to pieces if he had to. Matthar had circled behind him. He joined the chorus. â€Å"I pledge my life and honor to the Night’s Watch.† Jon kicked his mare, spinning her in a circle. The boys were all around him now, closing from every side. â€Å"For this night . . . † Halder trotted in from the left. † . . . and all the nights to come,† finished Pyp. He reached over for Jon’s reins. â€Å"So here are your choices. Kill me, or come back with me.† Jon lifted his sword . . . and lowered it, helpless. â€Å"Damn you,† he said. â€Å"Damn you all.† â€Å"Do we have to bind your hands, or will you give us your word you’ll ride back peaceful?† asked Halder. â€Å"I won’t run, if that’s what you mean.† Ghost moved out from under the trees and Jon glared at him. â€Å"Small help you were,† he said. The deep red eyes looked at him knowingly. â€Å"We had best hurry,† Pyp said. â€Å"If we’re not back before first light, the Old Bear will have all our heads.† Of the ride back, Jon Snow remembered little. It seemed shorter than the journey south, perhaps because his mind was elsewhere. Pyp set the pace, galloping, walking, trotting, and then breaking into another gallop. Mole’s Town came and went, the red lantern over the brothel long extinguished. They made good time. Dawn was still an hour off when Jon glimpsed the towers of Castle Black ahead of them, dark against the pale immensity of the Wall. It did not seem like home this time. They could take him back, Jon told himself, but they could not make him stay. The war would not end on the morrow, or the day after, and his friends could not watch him day and night. He would bide his time, make them think he was content to remain here . . . and then, when they had grown lax, he would be off again. Next time he would avoid the kingsroad. He could follow the Wall east, perhaps all the way to the sea, a longer route but a safer one. Or even west, to the mountains, and then south over the high passes. That was the wildling’s way, hard and perilous, but at least no one wouid follow him. He wouldn’t stray within a hundred leagues of Winterfell or the kingsroad. Samwell Tarly awaited them in the old stables, slumped on the ground against a bale of hay, too anxious to sleep. He rose and brushed himself off. â€Å"I . . . I’m glad they found you, Jon.† â€Å"I’m not,† Jon said, dismounting. Pyp hopped off his horse and looked at the lightening sky with disgust. â€Å"Give us a hand bedding down the horses, Sam,† the small boy said. â€Å"We have a long day before us, and no sleep to face it on, thanks to Lord Snow.† When day broke, Jon walked to the kitchens as he did every dawn. Three-Finger Hobb said nothing as he gave him the Old Bear’s breakfast. Today it was three brown eggs boiled hard, with fried bread and ham steak and a bowl of wrinkled plums. Jon carried the food back to the King’s Tower. He found Mormont at the window seat, writing. His raven was walking back and forth across his shoulders, muttering, â€Å"Corn, corn, corn.† The bird shrieked when Jon entered. â€Å"Put the food on the table,† the Old Bear said, glancing up. â€Å"I’ll have some beer.† Jon opened a shuttered window, took the flagon of beer off the outside ledge, and filled a horn. Hobb had given him a lemon, still cold from the Wall. Jon crushed it in his fist. The juice trickled through his fingers. Mormont drank lemon in his beer every day, and claimed that was why he still had his own teeth. â€Å"Doubtless you loved your father,† Mormont said when Jon brought him his horn. â€Å"The things we love destroy us every time, lad. Remember when I told you that?† â€Å"I remember,† Jon said sullenly. He did not care to talk of his father’s death, not even to Mormont. â€Å"See that you never forget it. The hard truths are the ones to hold tight. Fetch me my plate. Is it ham again? So be it. You look weary. Was your moonlight ride so tiring?† Jon’s throat was dry. â€Å"You know?† â€Å"Know,† the raven echoed from Mormont’s shoulder. â€Å"Know.† The Old Bear snorted. â€Å"Do you think they chose me Lord Commander of the Night’s Watch because I’m dumb as a stump, Snow? Aemon told me you’d go. I told him you’d be back. I know my men . . . and my boys too. Honor set you on the kingsroad . . . and honor brought you back.† â€Å"My friends brought me back,† Jon said. â€Å"Did I say it was your honor?† Mormont inspected his plate. â€Å"They killed my father. Did you expect me to do nothing?† â€Å"If truth be told, we expected you to do just as you did.† Mormont tried a plum, spit out the pit. â€Å"I ordered a watch kept over you., You were seen leaving. If your brothers had not fetched you back, you would have been taken along the way, and not by friends. Unless you have a horse with wings like a raven. Do you?† â€Å"No.† Jon felt like a fool. â€Å"Pity, we could use a horse like that.† Jon stood tall. He told himself that he would die well; that much he could do, at the least. â€Å"I know the penalty for desertion, my lord. I’m not afraid to die.† â€Å"Die!† the raven cried. â€Å"Nor live, I hope,† Mormont said, cutting his ham with a dagger and feeding a bite to the bird. â€Å"You have not deserted—yet. Here you stand. If we beheaded every boy who rode to Mole’s Town in the night, only ghosts would guard the Wall. Yet maybe you mean to flee again on the morrow, or a fortnight from now. Is that it? Is that your hope, boy?† Jon kept silent. â€Å"I thought so.† Mormont peeled the shell off a boiled egg. â€Å"Your father is dead, lad. Do you think you can bring him back?† â€Å"No,† he answered, sullen. â€Å"Good,† Mormont said. â€Å"We’ve seen the dead come back, you and me, and it’s not something I care to see again.† He ate the egg in two bites and flicked a bit of shell out from between his teeth. â€Å"Your brother is in the field with all the power of the north behind him. Any one of his lords bannermen commands more swords than you’ll find in all the Night’s Watch. Why do you imagine that they need your help? Are you such a mighty warrior, or do you carry a grumkin in your pocket to magic up your sword?† Jon had no answer for him. The raven was pecking at an egg, breaking the shell. Pushing his beak through the hole, he pulled out morsels of white and yoke. The Old Bear sighed. â€Å"You are not the only one touched by this war. Like as not, my sister is marching in your brother’s host, her and those daughters of hers, dressed in men’s mail. Maege is a hoary old snark, stubborn, short-tempered, and willful. Truth be told, I can hardly stand to be around the wretched woman, but that does not mean my love for her is any less than the love you bear your half sisters.† Frowning, Mormont took his last egg and squeezed it in his fist until the shell crunched. â€Å"Or perhaps it does. Be that as it may, I’d still grieve if she were slain, yet you don’t see me running off. I said the words, just as you did. My place is here . . . where is yours, boy?† I have no place, Jon wanted to say, I’m a bastard, I have no rights, no name, no mother, and now not even a father. The words would not come. â€Å"I don’t know.† â€Å"I do,† said Lord Commander Mormont. â€Å"The cold winds are rising, Snow. Beyond the Wall, the shadows lengthen. Cotter Pyke writes of vast herds of elk, streaming south and east toward the sea, and mammoths as well. He says one of his men discovered huge, misshapen footprints not three leagues from Eastwatch. Rangers from the Shadow Tower have found whole villages abandoned, and at night Ser Denys says they see fires in the mountains, huge blazes that burn from dusk till dawn. Quorin Halfhand took a captive in the depths of the Gorge, and the man swears that Mance Rayder is massing all his people in some new, secret stronghold he’s found, to what end the gods only know. Do you think your uncle Benjen was the only ranger we’ve lost this past year?† â€Å"Ben Jen,† the raven squawked, bobbing its head, bits of egg dribbling from its beak. â€Å"Ben Jen. Ben Jen.† â€Å"No,† Jon said. There had been others. Too many. â€Å"Do you think your brother’s war is more important than ours?† the old man barked. Jon chewed his lip. The raven flapped its wings at him. â€Å"War, war, war, war,† it sang. â€Å"It’s not,† Mormont told him. â€Å"Gods save us, boy, you’re not blind and you’re not stupid. When dead men come hunting in the night, do you think it matters who sits the Iron Throne?† â€Å"No.† Jon had not thought of it that way. â€Å"Your lord father sent you to us, Jon. Why, who can say?† â€Å"Why? Why? Why?† the raven called. â€Å"All I know is that the blood of the First Men flows in the veins of the Starks. The First Men built the Wall, and it’s said they remember things otherwise forgotten. And that beast of yours . . . he led us to the wights, warned you of the dead man on the steps. Ser Jaremy would doubtless call that happenstance, yet Ser Jaremy is dead and I’m not.† Lord Mormont stabbed a chunk of ham with the point of his dagger. â€Å"I think you were meant to be here, and I want you and that wolf of yours with us when we go beyond the Wall.† His words sent a chill of excitement down Jon’s back. â€Å"Beyond the Wall?† â€Å"You heard me. I mean to find Ben Stark, alive or dead.† He chewed and swallowed. â€Å"I will not sit here meekly and wait for the snows and the ice winds. We must know what is happening. This time the Night’s Watch will ride in force, against the King-beyond-the-Wall, the Others, and anything else that may be out there. I mean to command them myself.† He pointed his dagger at Jon’s chest. â€Å"By custom, the Lord Commander’s steward is his squire as well . . . but I do not care to wake every dawn wondering if you’ve run off again. So I will have an answer from you, Lord Snow, and I will have it now. Are you a brother of the Night’s Watch . . . or only a bastard boy who wants to play at war?† Jon Snow straightened himself and took a long deep breath. Forgive me, Father. Robb, Arya, Bran . . . forgive me, I cannot help you. He has the truth of it. This is my place. â€Å"I am . . . yours, my lord. Your man. I swear it. I will not run again.† The Old Bear snorted. â€Å"Good. Now go put on your sword.†

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Flexibility - Essay Example It works in interrelation with different operational and transactional factors like workforce, technological capital, organizational systems and the concern as a whole. Flexibility allowed in the labor force earns due efficiency if it helps to augment the degree of commitment of organizational workforce. (Procter & Ackroyd, 2009, p. 495). Three main themes would be outlined in the paper, which can be given as follows. The concept of flexibility to be successful must be closely tied to high degree of organizational commitment. Present level of increased competition triggers the need of a flexible workforce who would rightly adapt to changes in level of demand and operational process. The function of flexibility earns success if the employees work together in a committed manner to achieve organizational goals (Guest, 1989.p.49). Moreover, flexibility of the labor force tends to identify the Human Resources Management as a strategic initiative, which helps the company to earn a distinct competitive advantage. Human Resource Management as a strategic function encompasses the different policies and end goals behind the proper management of the labor force. The strategic face of human resource management is likely needed in bigger firms with several departments and also in other multinational firms for maintaining a strong binding in the labor force. (Boxar, Peter & Purcell, 2003. p.50) In key connection to the concept of human resources management is the process of recruitment and selection of the right candidate to help achieve the organizational goals. Thus recruitment and selection procedures and methods must be devised keeping in mind the end goals. The modern day organization desires to bring in a lot of flexibility in their organizational procedure and management of human resources in the organization. Modern day companies observe that through a flexible workforce the company can achieve high levels of profit and

Free Essays - Boys to Men in The Red Badge of Courage :: The Red Badge of Courage

Boys to Men in Red Badge of Courage      The Civil War took more American lives than any other war in history.   It divided the people of the United States, so that in many families brother fought brother.   The four years of bloodshed left a legacy of grief and bitterness that remains in part even today.   The war started on April twelfth, 1861 in Charleston, South Carolina.   It ended four years later on April ninth, 1865.   Many people call this tragic conflict the War Between the States, the War of the Rebellion, the War of the Secession, or the War for southern Independence.   But regardless of what it is called, the war was a great turning point in American history.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   What is so interesting about Crane's Red Badge of Courage?   I found out that war turns boys into mature men, the real dialect and slang used during the war, and what it's like to be a soldier in the Civil War.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   The whole novel covers only two days in the life of Henry Flemming, the main character.   In that amount of time, war can turn a boy into a man.   It does not physically turn an individual into a grown man, but it mentally matures them.   War matures boys into a men is by experiencing new, unpredictable environments and adjusting to unfamiliar smells, sounds, and emotions.   Think about it, being there on a battlefield witnessing deaths of friends and comrades would have to have an effect on a human being.   Being in a war and to be around new faces, new personalities, confusion, and trauma would force one to adapt to an environment faster than you usually would.   Just imagine leaving your country home and entering a new and frightening world on a battlefield.   What can make one a hero or a coward?   Fears, emotions, thoughts, and feelings can be the factors that contribute towards the struggle.   As I read this novel I lived not only Henry's actions, but also his individual thoughts and feelings.There was shootin' here an' shootin' there, an' hollerin' here and hollerin' there, in th' damn darkness, until I couldn't tell t' save m' soul which side I was on (p.136, Crane).   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   By utilizing the soldiers talking in a dialect that was common during the war and using slang to represent certain words reflected the authors' emphasis on realism and descriptiveness.

Background Checks: Give People a Second Chance

On every application for employment, there is always a section that asks about whether or not a person has ever had an felony charges against them, and to explain what they were if so. Despite the fact that employers are not â€Å"supposed† to discriminate against a candidate based on something like felony charges, there is no real way to qualify whether or not such discriminatory practices were exhibited in the candidate selection process. I would think it stands to reason that most employers will take one look at that box checked â€Å"yes† and move that application to the â€Å"no† pile.And this is only one question. Nowadays, most professional and corporate employers will conduct background checks on job candidates. This can be a problem for a person who has made mistakes in their life but has changed their behaviors and is looking for honest employment, and this is why the practice of running full background checks is basically set up to continually punish t hose who have made mistakes in the past. According to Privacy Rights Clearinghouse, many â€Å"negative† records are expunged from employer background checks after 7 years under the Fair Credit Reporting Act (FCRA).This includes arrests over 7 years ago, criminal records compiled by law enforcement agencies, and bankruptcies over 10 years old. However, much of this is public record, and though a standard background check might not yield this information, there are plenty of private information brokers on the web that will track it down, and this information is often not verified by the broker (such as charges being dropped against a person who was arrested—the broker might report only the arrest). As Crane notes in â€Å"The ABCs of Pre-Employment Background Checks†: â€Å"Unfortunately, there is a lot of inaccurate information out there.Just like the mistakes that may pop up on your credit report, bad data can turn up in the course of a background check. And t his wrong information can cost you a job. † Not only is there a stunning lack of privacy in this age of electronics, there is also no guarantee that the information being reported is accurate, which causes immediate problems for the individual applying for the job. Also, despite the fact that, for example, arrests made over 7 years ago are not supposed to be reported in a background check, there is nothing stopping the employer from asking, â€Å"Have you ever been arrested?†, a question which acts as a double-edged sword for someone who had been arrested several years before. In the cases of individuals who might have something in their past that they’re not proud of, information that can cost them their fair opportunity for employment is readily available to potential employers, even if it the FCRA specifically rules against it. Because of these Internet-based information brokers, there is no guarantee that information that shouldn’t be reported isn†™t still getting into the hands of the employer, and this is information that creates an inherent bias against the candidate in the employer’s mind.Information about long-ago prior arrests, fiscal irresponsibility in the form of previous bankruptcies, and criminal records which are not part of the public domain are easily acquired in a background check, and potential employers use this information as a major strike against the candidate. There is plenty of other information that is legitimately acquired in the course of a background check that can be detrimental to the perceived character of the person applying for the job.Information such as driving records, credit reports, interviews with neighbors and former employers, medical records, court records, and drug test records (just to name a few) are all standard-practice as part of an employer background check. Checking the box that authorizes an employer to conduct a background check opens a door into a person’s pas t in ways they might not have initially considered and affecting their chances at employment in ways they might not even conceive.It is understandable that in the wake of 9/11 and as a result of a recent surge in lawsuits due to negligent hiring practices (in which an employee caused harm to others), employers are practicing greater caution in their hiring practices. But by going as full-throttle as they are with the extensive amount of information being made available to them, they are essentially weeding out candidates who are talented, qualified, and educated but who have a spot on their records which leads to automatic disqualification of consideration by potential employers.People deserve to have a second chance in life, especially when they have taken all of the steps necessary to better themselves. It is grossly unjust that a prior arrest or criminal charge, especially one that isn’t even supposed to be part of a standard background check, would follow a person for the rest of their working lives, making it impossible for them to work in a professional field (especially when the rules as set by the FCRA are moot in cases involving government positions or positions that pay $75,000 per year or more).Let’s say a person, Joe Doe, has an old petty larceny charge, which many states consider a misdemeanor, but then loses a potential job offer because of it. The system is set up to continually punish those who have made mistakes in their past. In the above example of the felony charge check box (and a â€Å"felony† can be as simple as extorting $2,000 or being caught urinating in public), there is no way to avoid checking â€Å"yes† when the proceeding background check will show all of the related information, and act as an automatic disqualification for a person’s employment.When background checks are so pervasive and INVASIVE, what other options or opportunities does a person have left? This is why the system needs to be ch anged, and tighter restrictions need to be placed on what information is made available to the public. No record older than 7 years—criminal, felony, bankruptcy, or otherwise—should be made available for anyone to see.Only in the cases of serious potential endangerment (such as the higher-level sex offenders) should records older than 7 years be made public; otherwise people are being continually punished for old mistakes that they have more than rectified by paying their dues (either with community service, probation, monetary repayment, etc. ). It isn’t just that a person shouldn’t lose an opportunity due to long-ago mistakes; the reality is that employers WILL and DO discriminate based on that.In order for people to have the second chance they deserve, the restrictions on background checks and public records need to be tightened, to protect people who are trying to rehabilitate themselves. Otherwise, there is no rehabilitation to be had because the cha nce is never really given. References Crane, Amy B. â€Å"The ABCs of Pre-Employment Background Checks. † Online. Available: www. bankrate. com Fair Credit Reporting Act. Online. Available: www. ftc. gov Privacy Rights Clearinghouse. Online. Available: www. privacyrights. org