You will see plenty of fractions on the GRE, but don’t worry; everything you need to know about them you learned in second grade. You must be able to add, subtract, multiply, divide, and compare fractions. Here are the basics, with a couple of neat tricks thrown in.
In grade school, you learned to find the lowest common denominator. That still works. The Bowtie method is a convenient way to find the common denominator.
It looks like this.
Just multiply across the bottom to get your common denominator. Multiply on the diagonal to figure out your numerators and then add across the top. It works the same way for subtracting.
Here’s another helpful tip. If you have a fraction with addition or subtraction in the numerator, and a single number or variable in the denominator, you can split your original fraction into two separate fractions.
The Bowtie method is also useful for comparing fractions; this comes in very handy on Quant Comp questions. Just multiply up on the diagonals to compare any two fractions. If you want to compare 
and 
, for example, multiply 5 by 12 and 8 by 7, then compare. The larger number, 60, belongs to the
larger fraction, . Make sure you do this work on your scratch paper and not in your head.
In general, get in the habit of reducing all fractions to their simplest forms; it will make your life easier. Before you do, however, have a quick look at the answer choices to make sure your fractions need to be reduced. You don’t want to do more work than necessary.
Remember the following rules:
, you can take fours out of both, not sevens. This is shown with the factoring and cancellation of the twos.
Dividing a fraction by a fraction is the same thing as multiplying the first fraction by the reciprocal of the second fraction. You may be able to do this in your head, but don’t. Take the extra two seconds to lay it out on your scratch paper. It won’t take you much more time, and you’re less likely to make a careless error.
Occasionally ETS will give you a question in fractions and the answers in decimals, or one side of a Quant Comp in decimals and the other side in fractions. To convert a fraction to a decimal, use long division.
Make sure you check your answer choices and eliminate as you go, so you don’t waste time doing extra work. You will rarely have to divide a fraction out to more than two decimal places.
When converting from a decimal to a fraction, think of the decimal point as a 1 that goes on the bottom of your new fraction; then count up the number of digits that come after the decimal point and add the same number of zeros after the 1.
When you multiply decimals, the answer must have the same number of decimal places as the total decimal places in the numbers you are multiplying. For example, if you multiply 0.4 by 0.2, the answer must have two places to the right of the decimal, because 0.4 and 0.2 have one decimal place each. The answer is 0.08. Just remember that when you multiply a decimal by a decimal, the answers will get pretty small pretty quickly.
When you divide a decimal into a decimal, write it out as long division and convert the divisor into a whole number.
Since 0.003 is a very small number, it makes sense that it will go into 0.2751 (which is close to 0.3) nearly a hundred times. In fact, if you were Ballparking, you would notice that to get from 0.003 to a number close to 0.3 you would have to move your decimal point to the right two spaces. That is the same as multiplying by 100, so you would be looking for an answer choice that’s close to 100. Because 0.2751 is a little bit less than 0.3, you want a number that’s a little bit less than 100.
How do you express 
as a percentage? 50 percent, right? How do you express as a decimal? 0.5, right? You may know that 25 percent, 
and 0.25 are all the same thing. They are all fractions and they all express a 
relationship. The first tip for mastering percentages is realizing that they are really just fractions.
These are the most common fraction, decimal, and percentage equivalents; learn them, live them, love them.
(Click here to view a larger image.)
Memorize these fractions and be comfortable switching from one format to another, because when a question asks you for 75 percent, it may be easier to think of the percentage as 
. When a Quant Comp asks you whether 
or 
is
bigger, it may be easier to think of them as 80 percent and 75 percent.
Complicated percentages are often expressed as word problems rather than math problems. For example, “42 is what percent of 28”? This problem can be translated, word for word, into a single-variable equation.
Here’s your translation guide.
|
Word |
Symbol |
|
percent |
/100 |
|
of |
* (times) |
|
what |
x, y, or z |
|
is, are, was, were |
= |
Your translation is 42 = 
× 28.
How often have you used this one? Your bill is $28.50. You want to tip 20 percent. You know that 10% = $2.85. Double it to get $5.70, and you have 20 percent. You only want to leave 15 percent? Okay, what is half of 10 percent? Let’s call it $1.43. Add that back to the 10 percent, and you have $4.28, or 15 percent. You can do this with any number to quickly calculate exact percentages or to quickly ballpark answers.
|
Number |
Percentage |
|
1,246 |
100% |
|
124.6 |
10% |
|
12.46 |
1% |
|
62.3 |
5% |
|
373.8 (10% × 3) |
30% |
|
398.72 (10% × 3 + 1% × 2) |
32% |
The last, and perhaps most common, method of quickly calculating percentages is to set up a ratio of part to whole. Remember that the word percent simply means of 100, so 42 percent means 42 parts out of a total of 100.
With this set-up, the variable could go anywhere. ETS might give you the percentage and ask you for the whole. For example, “42 is 60 percent of what”?
To solve, simply cross-multiply: 4,200 = 60x.
A question might ask you, “42 is what percent of 70”? In this case, the x goes over the 100.
Or a question might ask you, “What is 60 percent of 70”? In this case you know the percentage and the total, but not the part.
Cross-multiply and you can solve. You can always put a percentage into this format.
For more practice and a more in-depth look at The Princeton Review math techniques, check out our student-friendly guidebook, Cracking the GRE.
