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Fractions are usually though not always best reduced as far as possible before they are multiplied by anything in GMAT questions You could burn up a lot of time trying to work with a fraction like 210 2772 So the first step when you see a mean looking fraction is to figure out ways to simplify it There are four rules that you can follow, generally in order: 1 Try to divide both the top and bottom by 2 This is called reducing the fraction by 2 Two is the first prime number, so it is always where you should start If the number is even, then it s divisible by 2 Do this as many times as possible In this case, that yields 210 2 = 105 2772 2 1386 2 Then try to divide both the top and the bottom by 3 (especially if reducing by 2 didn t work) A number will be divisible by 3 if the sum of its digits is a multiple of 3 In this case, 105: 1 + 0 + 5 = 6 and 6 is a multiple of 3, since 6 3 = 2 1386: 1 + 3 + 8 + 6 = 18 and 18 is a multiple of 3, since 18 3 = 6
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So we know that 3 is a factor of both the numerator and the denominator; therefore, reducing by 3 yields 105 3 = 35 1386 3 462 3 Next, try to divide both the top and the bottom by 5 If a number ends in 5 or 0, it s divisible by 5 Here, we could take it out of the numerator: 35 5 but 462 is not divisible by 5 462 5 4 Finally try to divide both the top and the bottom by 7: 35 7 = 5 462 7 66 And now we have a fraction that isn t so hard to work with If these four steps haven t reduced the number to a workable level, you could consider whether it is divisible by other primes, such as 11 or 13 If the number is that complicated, though, check over the answer choices to see whether you really need to reduce the fraction any further; if the answer choices themselves contain unwieldy fractions, then maybe further reduction is unnecessary If the number is really messy, you also may consider whether there might be an easier way to solve the problem
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There is a time to work with decimals, and a time to work with fractions For example, if a question asks you: If 375% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class A 110 B 330 C 550 D 430 E 880 You could multiply 0375 880, but you could probably work the problem faster if you realize that 0375 = 3 8 then you could multiply 3 880 = 3 880 = 3 880 = 3 110 = 330 8 8 8
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Remember that the question asked how many students are NOT enrolled in a biology class, so don t forget to subtract: 880 330 = 550 which is answer choice C Either method, multiplying by a decimal or by a fraction, works; the key is that if the quicker method can save you a few seconds here, those seconds might be the difference between a right answer and a wrong answer on a harder question near the end of the test The rule of thumb is that if the answer choices are in decimals, you should probably work the problem with decimals, and if the answer choices contain fractions, then you should stick with fractions If the answer choices do not steer you in either direction, go with the one that appears simpler and faster There are some equivalences between fractions and decimals that can save you time if you remember them for the test: 1/8 1/4 3/8 1/2 5/8 3/4 7/8 = = = = = = = 0125 025 0375 05 0625 075 0875 1/100 = 001 1/50 = 002 1/25 = 004 1/20 = 005 1/10 = 01 1/3 = 03333 2/3 = 06666
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