Complete Guide to Fractions and Ratios on SAT Math

Complete Guide to Fractions and Ratios on SAT Math SAT / ACT Prep Online Guides and Tips You likely had your first taste of working with fractions sometime in elementary school, though it's probably been a while since you've had to deal with how they shift, change, and interact with one another. To refresh, fractions and ratios are both used to represent pieces of a whole. Fractions tell you how many pieces you have compared to a potential whole amount (3 red marbles in a bag of 5, for example), while ratios compare pieces to each other (3 red marbles to 2 blue marbles) or, more rarely, pieces to the whole amount (again, 3 red marbles in 5 total). If this sounds complicated to you right now, don’t worry! We will go through all the principles behind fractions and ratios in this guide. If this seems easy to you right now, definitely check out the practice problems at the end of the guide to make sure you have mastered all the different kinds of fraction and ratio problems you’ll see on the test. The SAT likes to present familiar concepts in unfamiliar ways, so don’t let your mastery of fractions lead you to make assumptions about how you’ll see fractions and ratios on the test. No matter how comfortable you are (or are not) with fractions and ratios right now, this guide is for you. Here, we will go through the complete breakdown of fractions and ratios on the SAT- what they mean, how to manipulate them, and how to answer the most difficult fraction and ratio problems on the SAT. This Guide This guide is seperated into two distinct categories- everything you need to know about fractions and everything you need to know about ratios. For each section, we will go through the ins and outs of what fractions and ratios mean as well as how to manipulate and solve the different kinds of fraction and ratio problems you'll see on the SAT. We will also breakdown how you can tell when an SAT problem requires a ratio or a fraction and how to set up your approach these kinds of problems. At the end, you will be able to test your knowledge on real SAT math questions. The more you prep for the SAT, the more your brain can be Swiss-army-knife-ready for any question the test can throw at you. 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). A pizza is divided into 8 pieces. Kyle ate 3 pieces. What fraction of the pizza did he eat? He ate $3/8$ths of the pizza. 3 is the numerator (top number) because he ate that many pieces of the whole, and 8 is the denominator (bottom number) because there are 8 pieces total (the whole). Math is always more fun when it's delicious. Special Fractions A number over itself equals 1 $3/3=1$ $10/10=1$ $(a+b)/(a+b)=1$ A whole number can be expressed as itself over 1 $5=5/1$ $22/1=22$ $(a+b)/1=a+b$ 0 divided by any number is 0 $0/17=0$ $0/(a+b)=0$ There is one exception to this rule: $0/0=\undefined$. The reason for this lies in the next rule. 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. Reducing Fractions If both the numerator and the denominator have a common factor (a number they can both be divided by), then the fraction can be reduced. For the purposes of the SAT, you will need to reduce your fractions to get to your final answer. To reduce a fraction, you must divide both the numerator and the denominator by the same amount. This keeps the fraction consistent and maintains the proper relationship between numerator and denominator. If your fraction is $3/12$, then it can be written as $1/4$. Why? Because both 3 and 12 are divisible by 3. $3/3=1$ and $12/3=4$. So your final fraction is $1/4$ Now let's figure out how to perform the four basic math functions on fractions. 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. $4/15+2/15=6/15$ But you CANNOT add or subtract fractions if your denominators are unequal. $4/15+2/5=?$ 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. In the case of $4/15+2/5$, a common multiple of the denominators 15 5 is 15. When you find a common multiple of the denominators, you must multiply both the numerator and the denominator by the amount it took to achieve that number. Again, this keeps the fraction (the relationship between numerator and denominator) consistent. Think of it as the opposite of reducing a fraction. To get to the common denominator of 15, $4/15$ must be multiplied by $1/1$ Why? Because 15*1=15. $(4/15)(1/1)=4/15$. The fraction remains unchanged. To get to the common denominator of 15, $2/5$ must be multiplied by $3/3$. Why? Because 5*3=15. $(2/5)(3/5)=6/15$. Now we can add them, as they have the same denominator. $4/15+6/15=10/15$ We can further reduce $10/15$ into $2/3$ because both 10 and 15 are divisible by 5. So our final answer is $2/3$. Multiplying Fractions Multiplying fractions is a bit simpler than adding or dividing fractions. There is no need to find a common denominator- you 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. $1/4*2/3=(1*2)/(4*3)=2/12$ And again, we reduce our fraction. Both the numerator and the denominator are divisible by 2, so our final answer becomes: $1/6$ Special note: you can speed up the multiplication and reduction process by finding a common factor of your cross multiples before you multiply. $1/4*2/3$ = $1/2*1/3$. Why? Because both 4 and 2 are divisible by 2, we were able to reduce the cross multiples before we even began. This saved us time in reducing the final fraction at the end. So now we can simply say: $1/2*1/3=1/6$. No need to further reduce- our answer is complete. Take note that reducing cross multiples can only be done 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 multiples- you can 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. 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. ${2/3}à ·{3/4}$ = $2/3*4/3$ (we took the reciprocal of $3/4$, which means we flipped the fraction upside down to become $4/3$) $2/3*4/3=8/9$ But what happens if you need to divide a fraction by a whole number? If a cake is cut into thirds and each third is cut into fourths, how many pieces of cake are there? *** We start out with $1/3$ of a cake and we need to divide each third 4 more times. Because 4 is a whole number, it can be written as $4/1$. This means that its reciprocal is $1/4$. $1/3à ·4$ = $1/3*1/4=1/12$ Our denominator (the whole) is 12. This means there will be 12 pieces total in the cake. 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.) $4/5$ = 4/5 = 0.8 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. If $j/k=32$ and $k=3/2$, what is the value of $1/2j$ ? *** As you can see, there are two ways to approach this problem- using fractions and using decimals. We’ll look at both ways. If you were to use fractions, you would set up the problem as a fraction division problem. $k=3/2$ So $j/k=j/{3/2}$ $j/{3/2}$ = $j*2/3$ (remember, we take the reciprocal when we divide) So our full problem looks like this: $2/3*j=32$ Now we must divide 32 by $2/3$ in order to bring it over to the other side and isolate j. This means we need to take the reciprocal yet again. So ${32}/{2/3}$ = $32*3/2=96/2=48$ $j=48$ Now, for the final step, we must take $1/2$ of j. (Note: to "take $1/2$" is the same thing as multiplying by $1/2$.) $48*{1/2}=48/2=24$ Our final answer is 24. Alternatively, we could save ourselves the headache of using fractions and reciprocals and simply use decimals instead. We know that $k=3/2$. Instead of keeping the fraction, let us convert it into a decimal. $3à ·2=1.5$ So $k=1.5$ $j/k=32$ $j/1.5=32$ When you multiply both sides by 1.5, you get: $j=(32)(1.5)=48$ $j=48$ And ${1/2}j={1/2}(48)=24$ So again, our final answer is 24. Percentages After you convert your fraction to a decimal, you can also turn it into a percentage (if needed). So 0.8 from can also be written as 80%, because 0.8*100=80. A pie chart is a useful way of showing relative sizes of fractions and percentages. This shows just how large a fraction $7/10$ (or 70%) truly is. Mixed Fractions Sometimes you may be given a mixed fraction on the SAT. A mixed fraction is a combination of a whole number and a fraction. For example, 7$3/4$ is a mixed fraction. We have a whole number, 7, and a fraction, $3/4$. 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 ${\the \new \numerator}/{\the \original \denominator}$. 7$3/4$ (7)(4)=28 28+3=31 So your final answer = $31/4$ You must convert mixed fractions into fractions in order to multiply, divide, add, or subtract them with other fractions. In this problem, we began with 5 gallons of water and we ended with 2$1/3$. We must figure out how many gallons we used. 5−2 $5-2{1/3}$ First, let’s get our mixed fraction into a regular fraction. 2$1/3$ = ${[(2*3)+1]}/3={7/3}$ $5/1-7/3$ Now, we need to give each fraction the same denominator. We'll do this by converting $5/1$ into a new fraction with a denominator of 3. $5/1*3/3=15/3$ Finally, we can find the difference between the amounts. $15/3-7/3=8/3$ So we have used up $8/3$rds of the water. Now let’s count how many times the pail was emptied to use up that $8/3$rds of the total water. If you count the dots, the pail was emptied 8 times (the first dot does not count as a time it was emptied- that is merely our starting point). Because the same amount of water was removed each time, we must divide our emptied water by 8. ${8/3}à ·{8/1}$ = $8/3*1/8$ We can now either reduce the cross-multiples (because this is a multiplication problem), which would give us: $8/3*1/8$ = $1/3*1/1$ $1/3*1/1=1/3$ Or we can multiply through and then reduce afterwards: $8/3*1/8=8/24$ $8/12=1/3$ Either way, our final answer is $1/3$; each trip removed $1/3$ of a gallon of water from the tank. Now that we've broken down all there is to know about SAT fractions, let's take a look at their close cousin- the ratio. This shape is called the "golden ratio" and has been studied for thousands of years. It has applications in geometry, nature, and architecture. What are Ratios? Ratios are used as a way to compare one thing to another (or multiple things to one another). If Leslie has 5 white socks and 2 red socks, the white socks and the red socks have a ratio of 5 to 2. Expressing Ratios Ratios can be written in three different ways: A â€Å'to â€Å'B A:B $A/B$ No matter which way you write them, these are all ratios comparing A to B. 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: aâ€Å'part:a â€Å'different â€Å'part OR aâ€Å'part:theâ€Å' whole Because ratios compare values, they can either compare individual pieces to one another or an individual piece to the whole. If Leslie has only 5 white socks and 2 red socks in a drawer, the ratio of white socks to all the socks in the drawer is 5 to 7. (Why 7? Because there are 5 white and 2 red socks, so together they make 5+2=7 socks total.) Some of the many uses of ratios in action (in this case, the ratios are- a part: a different part). Reducing Ratios Just as fractions can be reduced, so too can ratios. Kyle has a stamp collection. 45 of them have pictures of daisies and 30 of them have pictures of roses. What is the ratio of daisy stamps to rose stamps in his collection? *** Right now, the ratio is $45:30$. But they have a common denominator of 15, so this ratio can be reduced. $45/15=3$ $30/15=2$ So the stamps have 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 4:3 can also be $4(2):3(2)=8:6$ $4(3):3(3)=12:9$ And so on. Marbles are to be removed from a jar that contains 12 red marbles and 12 black marbles. What is the least number of marbles that could be removed so that the ratio of red marbles to black marbles left in the jar will be 4 to 3? *** Right now, there are an equal amount of marbles, so the ratio is 12:12 (or 1:1) We know that we have an end ratio of 4:3 that we want to achieve and that each side of the ratio has to be multiplied (or divided) by the same amount to keep the ratio consistent. We want to remove as few marbles as possible, so let us imagine that 4:3 is a reduced ratio. That means we need to see how many total marbles the reduced ratio of 4:3 could possibly be. So both 4 and 3 have to be multiplied by the same amount to maintain their ratio and yet achieve a higher number of total marbles than just their 7 (4+3=7). We can see that 12 is divisible by 4, so the red marbles could conceivably remain unchanged in order to get a new ratio of 4:3. $12/4=3$ Because 4 can go evenly into 12, this will give us the fewest amount of marbles taken away. Because the 4 is multiplied 3 times to get 12, we know that both 4 and 3 must be multiplied by 3 to keep a new ratio of 4:3 consistent. To find the new number of black marbles, we take 3*3=9. The new amount of black marbles has to be 9. And because our red marbles remain the same (12), we must take only 3 marbles away from the total number of marbles (Why? Because 12â€Å' blackâ€Å' marbles−3 â€Å'blackâ€Å' marbles=9â€Å' blackâ€Å' marbles) So our final answer is 3, we must take 3 black marbles away to get a new ratio of 4:3 of red marbles to black marbles. Finding the Whole If you are given a ratio comparing two parts (piece:anotherâ€Å'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 4:5 can be: $4(1):5(1)=4:5$ $4(2):5(2)=8:10$ And so on, just as we did above. But this means we could also represent 4:5 as: $4x:5x$ 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. $4x+5x=9x$. The total amount is 9x. In this case, we don’t have any more information, but we know that the total must be divisible by 9. So let’s take a look at another problem. Teyvon has a basket of eggs that he is going to sell. There are two different kinds of eggs in the basket- white and brown. The brown eggs are in a ratio of 2:3 to the white eggs. What is NOT a possible number of eggs that Teyvon can have in the basket? A) 5 B 10 C) 12 D) 30 E) 60 *** In order to find out how many eggs he has total, we must add the two pieces together. So 2+3=5 This means that the total number of eggs in the basket has to either be 5 or any multiple of 5. Why? Because 2:3 is the most reduced form of the ratio of eggs in the basket. This means he could have: $2(2):3(2)=4:6$ eggs in the basket (10 eggs total) $2(3):3(3)=6:9$ eggs in the basket (15 eggs total) And so forth. We don’t know exactly how many eggs he has, but we know that it must be a multiple of 5. This means our answer is C, 12. There is no possible way that he can have 12 eggs in the basket. Now that we are armed with knowledge of fractions and ratios, we must follow the right steps to solve our problems. How to Solve Fraction, Ratio, and Rational Number Questions Now that we have discussed how fractions and ratios work indivisually, let's look at how you'll see them on the test. 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 "___ to ___† Explicitly use the word "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. A total of 120,000 votes were cast for 2 opposing candidates, Garcia and Pà ©rez. If Garcia won by a ratio of 5 to 3, what was the number of votes cast for Pà ©rez? (A) 15,000 (B) 30,000 (C) 45,000 D) 75,000 (E) 80,000 *** As you can see, our ratio of 5 to 3 has been greatly reduced (neither of those numbers is in the tens of thousands). We know that there are a total of 120,000 votes, so we need to determine the number of votes for each candidate. Let’s first add our ratio pieces together. 5:3 = 5+3=8 Because 8 is much (much) smaller than 120,000, we know that 8 is not our whole. But 8 is the factor of our whole. ${120,000}/8=15,000$ So if we think of 15,000 as one component (a replacement for our variable, $x$), and Garcia and Pà ©rez have a ratio of 5 components to 3 components, then we can find the total number of votes per candidate. G:P=5:3 = $5x:3x$ 5*15,000=75,000 3*15,000=45,000 So Garcia earned 75,000 votes and Pà ©rez earned 45,000 votes. (You can even confirm that this must be the correct number of votes each by making sure they add up to 120,000. 75,000+45,000=120,000. Success!) So our final answer is C, Pà ©rez earned 45,000 votes. #3: When in doubt, try to use decimals Decimals can make it much easier to work out problems (as opposed to using fractions). So do not be afraid to convert your fractions into decimals to make life easier. #4: Remember your special fractions Always remember that a number over 1 is the same thing as the original number, and that a number over itself = 1. If $h$ and $k$ are positive numbers and $h+k=7$ then ${7-k}/h=$ (A) 1 (B) 0 (C) -1 (D) $h$ (E) $k-1$ *** Here we have two equations: $h+k=7$ and ${7-k}/h$ So let us manipulate the first. $h+k=7$ can be re-written as: $h=7−k$ (Why? We simply subtracted $k$ from either side) So now we can replace the $(7−k)$ from the second equation with $h$, as the two terms are equal. This leaves us with: $h/h$ And we know that any number over itself = 1. So our final answer is A, 1. Now, let's put your knowledge to the test! Test Your Knowledge #1: Flour, water, and salt are mixed by weight in the ratio of 5:4:1, respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required? (A) $1/4$ (B) $1/2$ (C) $3/4$ (D) 1 (E) 2 #2: #3: Which of the following answer choices presents the fractions $5/4$, $4/3$, $19/17$, $13/12$, and $7/6$ in order from least to greatest? (A) $19/17$, $7/6$, $13/12$, $4/3$, $7/6$, $5/4$ (B) $4/3$, $5/4$, $7/6$, $19/17$, $13/12$ (C) $13/12$, $7/6$, $19/17$, $5/4$, $4/3$ (D) $19/17$, $13/12$, $5/4$, $7/6$, $4/3$ (E) $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ Answers: B, D, E Answer Explanations: #1: This question is a perfect example of when to find the whole of the pieces of the ratio. Flour, water, and salt are in a ratio of 5:4:1, which means that the whole is: $5x+4x+1x=10x$ So $10x$ is our whole. We want 5 pounds of the recipe, so we must convert $10x$ to 5. $10x=5$ $x=1/2$ Our variable is $1/2$ . Now, we are looking for the amount of salt to use when we started out with $1x$. So let us replace our $x$ with the value we found for it. $1x$ $1(1/2)$ $1/2$ This means we need $1/2$ a pound of salt to make 5 pounds of the mixture. Our final answer is B, $1/2#. #2: For this question, we must find a non-zero integer for t in which $x+{1/x}=t$, where $x$ is also an integer. We know, based on our special fractions, that the only possible way to get a whole number in fraction form is to have our demoninator equal 1 or -1. This means that x cannot possibly be anything other than 1 or negative 1. (Why? If x were anything else but 1, we would end up with a mixed fraction. For example, if x=2, then we would have: $2+{1/2}$. If $x=3$, we would have: $3+{1/3}. And so on. The only way to get an integer value for $t$ is when $x=1$.) So let us try replacing our $x$ value with 1. $x+{1/x}=t$ $1+{1/1}=2$ $t=2$ Well, $t$ could possibly equal 2, but this is not one of our answer choices. So now let us replace $x$ with -1 instead. $x+{1/x}=t$ $-1+{1/-1}=-2$ t=−2 Success! We have found a value for $t$ that matches one of our answer choices. Our final answer is D, $t=−2$ #3: For a problem like this (one that has you order fractions by size), it is usually a good idea to break out the decimals. But we will go through how to solve it using both methods of fractions and decimals. Solving with decimals: To solve with decimals, simply divide each numerator by its denominator to get the decimal. Then, order them in ascending order (as we are told). $5/4=1.25$ $4/3=1.333$ $19/17=1.12$ $13/12=1.08$ $7/6=1.16$ We can see here that the order from least to greatest is: 1.08, 1.12, 1.16, 1.25, 1.33 Which, converted back to their fraction form is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So our final answer is E. Alternatively, we can solve using fractions. Solve using fractions: Let us find a common denominator between all the numerators. A quick way to do this is by multiplying the two largest numerators together. (It may not be the least common denominator, but it'll do for our purposes.) $17*12=204$ Now let's make sure that the other denominators can go evenly into 204 as well. $204/6=34$ $204/4=51$ $204/3=68$ Perfect! Now let us convert all of our fractions. $5/4={5(51)}/{4(51)}=255/204$ $4/3={4(68)}/{3(68)}=272/204$ $19/17={19(12)}/{17(12)}=228/204$ $13/12={13(17)}/{12(17)}=221/204$ $7/6={7(34)}/{6(34)}$ Now that they all share a common denominator, we can compare and order their numerators. So, in ascending order, they would be: $221/204$, $228/204$, $238/204$, $255/204$, $272/204$ Which, when converted back to their original form, is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So again, our final answer is E. I think a nap is in order- don't you? Take-Aways Fractions and ratios may look tricky, but they are merely ways to represent the relationships between pieces of a whole and the whole itself. Once you know what they mean and how they can be manipulated, you’ll find that you can tackle most any fraction or ratio problem the SAT can throw at you. But always remember- though ratios and fractions are related, do not get them mixed up on the SAT! The vast majority of the time, the ratios they give you will compare parts to parts and the fractions will compare parts to the whole. It can be easy to make a mistake during the test, so don’t let yourself lose a point due to careless error. What’s Next? You've conquered fractions and you've decimated ratios and now you're eager for more, right? Well look no further! We have guides aplenty for the many math topics covered on the SAT, including probability, integers, and solid geometry. Feel like you're running out of time on the SAT? Check out our article on how to finish your math sections before time's up. Don't know what score to aim for? Make sure you have a good grasp of what kind of score would best suit your goals and current skill level, and how to improve it from there. Angling to get an 800 on SAT Math? Look to our guide on how to get a perfect score, written by a perfect SAT scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice 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:

Quotes From William Shakespeares Romeo and Juliet

Quotes From William Shakespeares Romeo and Juliet Romeo and Juliet,  one of Shakespeares iconic tragedies,  is a play about star-crossed lovers, their romance doomed from the start. It is one of the most famous plays of the English Renaissance, consistently taught and staged at high schools and colleges. As their families feud to the death, Romeo and Juliet, the two young lovers, are caught between disparate worlds. The unforgettable play is filled with fights, secret marriages, and untimely deaths–along with some of Shakespeares most famous lines. Love and Passion The romance of Romeo and Juliet is perhaps the most famous in all of literature. The young lovers, despite their families objections, will do anything to be together, even if they must meet in secret. During their private rendezvous, the characters give voice to some of Shakespeares most romantic speeches. What sadness lengthens Romeos hours? / Not having that, which, having, makes them short. / In love? / Out / Of love? Out of her favor, where I am in love. [Act 1, Scene 1] One fairer than my love? The all-seeing sun / Neer  saw her match since first the world begun. [Act 1, Scene 2] Did my heart love till now? Forswear it, sight! / For I neer saw true beauty till this night. [Act 1, Scene 5] My bounty is as boundless as the sea / My love as deep; the more I give to thee, / The more I have, for both are infinite. [Act 2, Scene 2] Good Night, Good night! Parting is such sweet sorrow, that I shall say good night till it  be  morrow. [Act 2, Scene 2] See, how she leans her cheek upon her hand! /  O that I  were  a glove upon that hand, /  that I might touch that cheek! [Act 2, Scene 2] These violent delights have violent ends / And in their triumph die, like fire and powder, / Which as they kiss consume. [Act 2, Scene 3] Family and Loyalty Shakespeares young lovers come from two families–the Montagues and the Capulets–that are sworn enemies of each other. The clans  have kept alive their ancient grudge for years. In their love for each other, Romeo and Juliet have each betrayed their family name. Their story shows what happens when this sacred bond is broken. What, drawn, and talk of peace? I hate the word, / As I hate hell, all Montagues, and thee. [Act 1, Scene 1] O Romeo, Romeo! wherefore art thou Romeo? / Deny thy father and refuse thy name. / Or if thou wilt not, be but sworn my love / And Ill no longer be a Capulet. [Act 2, Scene 2] â€Å"Whats in a name? that which we call a rose  /  By any other name would smell as sweet.†Ã‚  [Act 2, Scene 2] A plague o both your houses! [Act 3, Scene 1] Fate From the very beginning of the play, Shakespeare announces Romeo and Juliet as a story of destiny and fate. The young lovers are star-crossed, doomed to ill fortune, and their romance can only end in tragedy. The play unfolds with an inevitability reminiscent of Greek tragedy, as forces in motion slowly crush the young innocents who try to defy them. Two households, both alike in dignity  /  In fair Verona, where we lay our scene  /  From ancient grudge break to new mutiny  /  Where civil blood makes civil hands unclean.  /  From forth the fatal loins of these two foes  /  A pair of star-crossd lovers take their life  /  Whose misadventured piteous overthrows  /  Do with their death bury their parents strife.†Ã‚  [Prologue] This days black fate on more days doth depend: / This but begins the woe others must end. [Act 3, Scene 1] â€Å"Oh, I am fortunes fool!†Ã‚  [Act 3, Scene 1]

Free Essays on Dell

Dell Computer Corporation SYNOPSIS In this report an examination will be made of the production and logistics system of Dell Computer Corporation. The important aspects of Dell’sEmphasis will be placed on the following: How effective is the firms resource planning procedures? product/ service The key difficulties - potentialDells internal and external logistics process How technologies are beingpoints of failure in the Dell’s logistics process used or can be used to make the logistics function more efficient/effective? What is Dell Computers all about? Michael Dell founded Dell Computer Corporation in 1984 having only $1000 start-up capital. To date, his business has grown to become the second largest computer systems producer in the world, with average daily sales of more than $5 million. The ‘hub’ of Dells production system is based in the U.S (Round rock, Texas), while other factories are located in Nashville, Tennessee, Limerick, (Ireland), Penang, Malaysia, Xiamen, Chin a and Eldorado do Sul, Brazil. Dell has offices in thirty-four countries around the world and sells its products and services in more than one hundred and seventy countries. The table below provides a break down of Dells global market growth and position. Monetary values are quoted in US$ in millions. Continent Market Position Net Revenue as at January 28/2000 Annual Growth Rate Dell Americas Dell Europe/Middle East/Africa Dell Asia Pacific and Japan 1 2 7 17879 5590 1796 48% 24% 52% According to Dells forecast it is estimated that total revenue will amount to US$33 billion this year, where US$20 billion will be as a result of online transactions. (1) In the Appendix of this report, a consolidated statement of income on Dells financial position for the year ending 28/1/00 is presented. The important aspects of Dells Product and Service Dells core competency lies in customising its product – computer hardwar... Free Essays on Dell Free Essays on Dell Dell Computer Corporation SYNOPSIS In this report an examination will be made of the production and logistics system of Dell Computer Corporation. The important aspects of Dell’sEmphasis will be placed on the following: How effective is the firms resource planning procedures? product/ service The key difficulties - potentialDells internal and external logistics process How technologies are beingpoints of failure in the Dell’s logistics process used or can be used to make the logistics function more efficient/effective? What is Dell Computers all about? Michael Dell founded Dell Computer Corporation in 1984 having only $1000 start-up capital. To date, his business has grown to become the second largest computer systems producer in the world, with average daily sales of more than $5 million. The ‘hub’ of Dells production system is based in the U.S (Round rock, Texas), while other factories are located in Nashville, Tennessee, Limerick, (Ireland), Penang, Malaysia, Xiamen, Chin a and Eldorado do Sul, Brazil. Dell has offices in thirty-four countries around the world and sells its products and services in more than one hundred and seventy countries. The table below provides a break down of Dells global market growth and position. Monetary values are quoted in US$ in millions. Continent Market Position Net Revenue as at January 28/2000 Annual Growth Rate Dell Americas Dell Europe/Middle East/Africa Dell Asia Pacific and Japan 1 2 7 17879 5590 1796 48% 24% 52% According to Dells forecast it is estimated that total revenue will amount to US$33 billion this year, where US$20 billion will be as a result of online transactions. (1) In the Appendix of this report, a consolidated statement of income on Dells financial position for the year ending 28/1/00 is presented. The important aspects of Dells Product and Service Dells core competency lies in customising its product – computer hardwar... Free Essays on Dell The computer industry has enjoyed a tremendous growth in the 80’s and 90’s. The introduction of the Internet to the public had a major impact on this growth. First, the Internet created a new environment to conduct business online. The Internet gave a way to new start-up companies to do business online, therefore increasing the demand for network of computers. Second, public dependency to the Internet increased while they found a convenient way of shopping online. Public dependency on computers to gain access to the Internet also increased the demand for computers. Except for the relatively few companies that have been somewhat successful in managing their businesses reasonably well, the first few years in the 2000’s have been a struggle for most companies in the industry due to unstable market, fierce competition and over saturation of the market. As PC sales slow worldwide, computer companies have embarked on a broad campaign to gain market share- by cutting prices, introducing new product lines, and forming alliances with companies that can help them broaden their capabilities. Among those who seem to be surviving and planning to take advantage of the economical situation, include Dell Computer Corporation, IBM, Gateway and the Apple Computer Company. The paper will study Dell Computer Corporation and its business model, including many aspects of direct marketing introduced by Dell Computers will be analyzed. Market segmentation, competition, and business opportunities will also be analyzed along with recommendations for business expansion. E-Commerce Electronic commerce is defined as the delivery of goods, services, information, or payments over computer networks or by any other electronic means (e-business, 2002) The e-commerce isn’t just for tech-savvy shoppers anymore, having broadened its appeal to a majority of the population, the average online customer now expects more and is a harder sell, much like the...

Analysis of Article about Aspects of the Media Essay

Analysis of Article about Aspects of the Media - Essay Example The two articles argue that in most cases, the content that is produced by the media is bias. This is the main point that the two articles seek to make. The claims that are made in the articles are however very different. Feldman is of the opinion that media bias has come up in recent years and as such, the consumer is now exposed to biased content as opposed to earlier years when the media had a tradition of ensuring objectivity in their reporting. Bias is, therefore, a product of contemporary media. Boring, however, is of the opinion that the media has never at any point tried to avoid bias, and has indeed always promoted it. According to him, bias is in the nature of media from the beginning. The two writers do agree that there is a presence of bias in the media. However, the article by Feldman asserts that the bias that is in the media news and reports is over and that the audience that is the consumer of this news is more likely to perceive host bias as well as story bias in the opinionated news of the media that they perceive in the non-opinionated news. The article by Boreing, on the other hand, promotes the opinion that the bias in the content of the media is in such a way that the consumer does not notice it as it is geared towards influencing his thoughts and actions. The two writers disagree on different points. The main point of disagreement is on when biased reporting in the media began. Boreing asserts that right from the beginning; the media has always been biased and has never actually made any attempts at objectivity. Feldman, on the other hand, suggests that bias in the media has come up in recent times as a result of changes in the presentation style of the cable news that has seen the news depart from the tradition of being objective. Lack of objectivity in the media is, therefore, a recent phenomenon according to Feldman. The lack of objectivity in the media according to Feldman has been promoted by the use of the cable news. This has seen the rise in the expression of explicit personal opinions and bias in the news coverage.  

Strategic plan for one of the companies listed on Forbes International Essay

Strategic plan for one of the companies listed on Forbes International Top Ten list - Essay Example In today’s modern era, every company strives to dominate its market. In order to gain any market segment, a company must have a business strategic plan implemented to achieve its goals. Each year Forbes.com comes with a list of top corporations that are excelling in their market. One of the firms that have made a dramatic impact in its industry is Toyota. Toyota is one of the few companies that has the honor to claim itself as â€Å"not only the best automaker in the world, but also maybe the best corporation†. This paper will discuss the strategic management of Toyota and its quest to become the market leader in its industry. One of the most unique strategic planning that Toyota has implemented is to employee top management positions from Japan. Although this move might not work for every corporation, Toyota has the reputation to preserve its brand reputation. From design to corporate decisions, all operations take place in Tokyo[2]. The reason for this is clearly expl ained by John Paul MacDuffee, a professor at local university as he states, â€Å"This is about a greater maturity about globalizing and transferring knowledge that Toyota certainly has at this point.†[2]. In addition, these executives decided to ask their suppliers to reduce their cost by 30%. Management understood that every little step taken by them will influence the company in the long-run. By building a solid environment of knowledge and design, Toyota is able to utilize mass production methods[1]. How is this achieved? Well, the company is a firm believer in the Just-in-time â€Å"lean production.† Toyota’s lean manufacturing system is a critical for its strategic planning by enhancing the flow of work [1]. In addition, it focuses to reduce the organization’s waste, which dramatically increases customer value. Moreover, it levels of production level which eliminates unevenness in its manufacturing system. Just-in-time improves organization's return on investment, quality, and efficiency[1]. Undoubtedly, much of the success that Toyota has enjoyed is due to this model that is collaborated and implemented through planning and executive models. The current strategic planning for Toyota is to introduce a new line of hybrid cars. As humanity progresses to the 21st century, society has becoming more environmental friendly. Hence, Toyota saw this as an opportunity to expand its line of cars. Hence, it decided to invest heavily in research and development in order to build hybrid-electric vehicles [3]. Toyota’s ability to fund in development was critical as it poured millions of dollars without hurting its capital budget. After years of researching, Toyota decided to aggressively showcase its new hybrid Camry and Highlander, two cars that are known for quality and durability [3]. However, it was met by a tough rival as Ford introduced its newest S.U.V at the same time where Toyota showcased its news Prius. While other companyà ¢â‚¬â„¢s struggled to design hybrid cars that produced revenue, Toyota was already enjoying decent profits. Interestingly enough, the company never attempts to make any bold of false promises as other companies. Toyota executives acknowledged the fact that gas prices will continue to rise as oil becomes scarce. Furthermore, it was clear that creating an automobile that was â€Å"environmental friendly† is clearly going to be the future of the industry[3]. Hence, by carefully forecasting the

Crime Analysis Why Does Detroit Have Such a High National Murder Rate Assignment

Crime Analysis Why Does Detroit Have Such a High National Murder Rate - Assignment Example In addition, the media placed Detroit as the 2nd city in terms of murder cases in the entire U.S (Fisher, 2013). However, in 2013 the city’s rate abridged significantly though this still equaled with New York statistics whose population is far beyond that of Detroit by 11 times (Crime statistics, 2013). Hence, has become Murder City having 333 homicides of all kinds in 2013 despite analysts contending that was the lowest figure compared to other studies (The Washington, 2014). Most murders occurred between acquaintances, with people involved either in criminal activities or in domestic violence as evidenced by statistics from previous years. Based on already compiled data, reports cite it is a common scenario for gang members to turn on each other. Drug deals going bad were another reason for murders between people who knew each other. For instance, two teenagers were shot and found dead lying on a field facedown after having purchased marijuana from their local supplier. There were reports of domestic violence whereby spouses killed each other, parents killing their children or children terminating lives of their parents. Logan, a police chief in Detroit, gave an example of a woman who stabbed her eight-year-old girl and cited it as a typical scenario experienced in 2012 (Fisher, 2013). Logan further contended America currently experiences increased cases related to gun shootings but Detroit is the epicenter. Gun violence is something very ordinary in Detroit as most people own guns either legally or illegally. According to FBI reports, gun assault increased tremendously over the past years whereby 532 armed crimes were reported for every 100, 000 residents in 2010. The city’s respective authority went ahead to devise a policy whereby people were to hand over their guns at a fee, no questions asked. Its purpose was to reduce the number of guns in Detroit. It was a great failure as gun-related crimes are still a big problem in the

Politics and war in Afghanistan during the novel Kite Runner Essay

Politics and war in Afghanistan during the novel Kite Runner - Essay Example Touted as the first Afghan novel written in English, Khaled Hosseini's The Kite Runner makes up part of the growing branch of Muslim American immigrant literature (along with Diana Abu-Jaber's Crescent and Laila Halaby's West of the Jordan , both published in 2003). Loosely autobiographical, The Kite Runner begins in the same well-off Kabul neighborhood in which the author grew up with his diplomat father and schoolteacher mother. The action then shifts to California, where the family resettled in the early 1980's after fleeing Afghanistan. Hosseini, a practicing physician, began the novel in March, 2001, and, working in the early morning hours, had it half-completed by September 11, 2001. The terrorist attacks which occurred on that day left him and other Muslim Americans feeling anxious about their safety and also turned his unfinished novel into a hot property. After making a successful preemptive bid, Riverhead Books asked Hosseini to revise the manuscript (rather extensively, it turned out) in just four weeks in late 2002, in order to capitalize on interest in Afghanistan during the United States' military action against the Taliban. The well-publicized novel appeared in the summer of 2003, just after American and world interest had shifted from Afghanistan to Iraq. Employing a simple but effective three-part structure, framed by chapters set in December, 2001, The Kite Runner begins where Arundhati Roy's Booker Prize-winning novel The God of Small Things (1997) ends, with an act of betrayal. Part 1 focuses on the formative years of its narrator-protagonist, especially his relationship with Hassan, who is at once his servant and friend. The two boys are linked in several important ways: Born just a year apart, they live in the same household and have nursed at the same breast (following Amir's mother's death in childbirth and Hassan's mother's having run away). The two are also divided-by physical ability, by temperament, by class, and most deeply by ethnicity, one a member of the majority Pashtuns, the other a despised Hazara. Hassan's devotion to Amir is both a sign of his sweet disposition and, more troubling, the result of an ingrained servant-class mentality. Amir is, if not quite devoted to his playmate then certainly attached (including in a way that Amir could never have imagined, for Hassan turns out to be his half brother). Amir's relatively privileged life, however, coupled with Hassan's self-sacrificing devotion, makes Amir cruel, albeit in petty, even passive ways. Amir's cruelty and weakness of character are thrown into higher relief when a third boy, Assef, arrives on the scene. "On the surface, he was the embodiment of every parent's dream but his eyes betrayed him. Beyond the faade, madness." Beyond Amir's facade there is neither madness nor maliciousness, only anxiety that derives, in large measure, from his not being manly enough to earn the love of his father, Baba, a successful, decidedly secular businessman highly respected for his business savvy, physical prowess, and charitable acts. Amir's character is a typical Afghani character of the contemporary society. His character has been delineated by the writer very carefully and according to the norms and standing customs and conventions of Afghan society of that time. The crisis,