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Shortcut for Converting Fractions to Percents

So, you’re working on a GMAT question that requires you to find a certain percent. After some work, you get to the point where you must convert 11/49 into an approximate percent. What do you do from here?

Well, as always, we should check the answer choices before performing any calculations. If the answer choices are sufficiently spread apart, we can use some estimation techniques.

Let’s say that the 5 answer choices are as follows:

(A) 19.8%

(B) 21.6%

(C) 22.4%

(D) 39.4%

(E) 40.6%

Since several answer choices are very close together, some rounding and estimation techniques may not work.

The technique we’ll examine relies on the observation that a fraction with 100 in the denominator is very easy to convert to a percent. For example, 19/100 = 19%, 72/100 = 72% and 123/100 = 123%

So, to convert 11/49 to a percent, we’ll find an equivalent fraction that has 100 in the denominator. In other words, we’ll find an equivalent fraction such that 11/49 = x/100.

To create an equivalent fraction, we multiply the numerator and denominator by the same value. So, what number must we multiply 49 by to get 100?

If we multiply 49 by 2, we get a product of 98. So, to get a product of 100, we must multiply 49 by a number a little bit bigger than 2. We’ll use the notation 2+ to denote a number a little bit bigger than 2.

At this point, we’ll multiply numerator and denominator by 2+ to get 11/49 = (11)(2+)/(49)(2+). The product (49)(2+) in the denominator equals 100, and the product (11)(2+) in the numerator equals 22+ (a number a little bit bigger than 22).

So, 11/49 = (22+)/100 = 22+%, which is a little bit more than 22%. When we check our answer choices, only answer choice C fits the bill. So, it must be the correct answer.   

Let’s try one more example.

To convert 15/34 to a percent, we’ll first find an equivalent fraction with 100 in the denominator. In other words, we’ll find an equivalent fraction such that 15/34 = x/100.

To create this equivalent fraction, we’ll take 15/34 and multiply the numerator and denominator by 3- (a number a little bit smaller than 3), to get 15/34 = (15)(3-)/(34)(3-). When we simplify, we get 15/34 = (45-)/100 = 45-%, which is a little bit less than 45%.