Why You Should Convert Fractions to Decimals on the GMAT

Certain skills help make the math portion of the GMAT much easier. For example, being at ease with multiplication and factoring can help you on all kinds of questions that aren’t even about multiples or factors. In fact, questions about one and only one topic are few and far between. A GMAT question will never ask you what 8 x 7 is explicitly, but it could easily ask you the area of a triangle with a base of 16 and a height of 7. (Recall that the formula for the area of a triangle is ½ Base x Height).

Similarly, a skill that comes up frequently on the GMAT is the ability to convert from fractions to decimals. If you see ½, you can easily convert this to 0.5. However, if the exam asks you 2/7, 8/9 or 3/8, could you convert these numbers into decimal and then use them to solve an overarching question? Not everyone is comfortable with these kinds of calculations, and yet understanding fractions is one of the biggest parts of the GMAT. (And yes, that pun was intended)

As a quick reminder, knowing the conversion for all single-digit fractions will help you save time on these questions, even if the question often asks for more than just a simple exchange from fraction to decimal. From one half to one fifth, these should be easy, so there are only a few fractions that are somewhat unfamiliar. As a quick review:

1/2: 0.500
1/3: 0.333
1/4: 0.250
1/5: 0.200
1/6: 0.167 (half of 1/3)
1/7: 0.143 (just need to know this one)
1/8: 0.125 (half of 1/4)
1/9: 0.111 (ninths always have the same number repeating periodic)

Now of course, questions often ask about a fraction other than 1/x, but if you know the base case, you can simply multiply to get to 2 or 3 or any other number. Again, you will never see a GMAT question that asks you “What is the decimal value of 1/7” (even if you’re scoring a 200). However you can definitely see a question like:

If x is the median of the set {9/2, 11/3, 28/9, 21/5, x}, x could be

(A) 16/5
(B) 17/5
(C) 4
(D) 30/7
(E) 31/7

This question would fall into the category of statistics, as it is primarily asking about the median of a set. However, if you know that the median is just the middle term of an ordered set, then the real difficulty of this question is putting the elements in ascending (or even descending) order. The fastest way to do this is probably to convert all the numbers into decimals and ranking them in that method.

This is probably easiest if we separate the integers from the fractions, which can be done in two parts.

9/2 = 8/2 + 1/2 = 4 1/2 = 4.5
11/3 = 9/3 + 2/3 = 3 2/3 = 3.67
28/9 = 27/9 + 1/9 = 3 1/9 = 3.11
21/5 = 20/5 + 1/5 = 4 1/5 = 4.2

The four numbers in order are thus really 3.11, 3.67, 4.2 and 4.5. The median (x) could be anywhere from 3.67 to 4.2. A cursory glance at the answer choices confirms that it must be 4. We can take the extra step of eliminating the other four choices by converting them using the same method:

(A) 16/5 = 15/5 + 1/5 = 3 1/5 = 3.2
(B) 17/5 = 15/5 + 2/5 = 3 2/5 = 3.4
(C) 4 = 4 = 4 = 4
(D) 30/7 = 28/7 + 2/7 = 4 2/7 = 4.29
(E) 31/7 = 28/7 + 3/7= 4 3/7 = 4.43

It’s worth mentioning that the GMAT characteristic of always having the answer choices in order will be maintained here, even if the order isn’t obvious due to different denominators.

Alternatively, if you’re a big fan of fractions, you can solve this question using only fractions. The downside is that the math becomes much more unwieldy. If I want to put halves, ninths and fifths on a common denominator, I need to put all these fractions on ninetieths.

You could rewrite the set

{9/2, 11/3, 28/9, 21/5, x}
as
{405/90, 330/90, 280/90, 378/90, x}

It is now easy to put these numbers in order: {280/90, 330/90, x, 378/90, 405/90}. The number x must now be between 330/90 and 378/90. The number 4 converts to 360/90, so you can see it fairly easily. However this process is more difficult and time-consuming than simply converting the numbers into decimals, but it will still work. Without a calculator, multiplying 21 by 18 may prove to be more hassle than it’s worth.

When it comes to fractions, generally being at ease with them and converting easily to and from decimals will help you get the correct answer on many different types of GMAT questions. Just because a question is asking about medians or areas or probability doesn’t mean that you won’t need to use your knowledge of fractions to solve the question. To paraphrase the seminal 80s cartoon G.I. Joe: Knowing is ½ the battle.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

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