GMAT Fractions From Scratch

Fractions sit inside almost every GMAT Quant question. Any time you multiply and divide, you are working with a fraction whether it looks like one or not. If you can do this arithmetic but it takes you thirty seconds, that is the problem this lesson solves.

The school method costs you time

School teaches you to multiply the numerators, multiply the denominators, then simplify what comes out. Multiply 3/4 by 8/9 and you get 24/36, then you break 24 into 3 × 4 × 2 and 36 into 4 × 3 × 3 and cancel.

You did the work, then undid it. On a timed exam you cannot afford both halves.

The faster route is to split the numbers into factors first. Write 8 as 4 × 2 and 9 as 3 × 3, cancel what appears on both sides, and the answer falls out as 2/3 with no multiplication at all. This one habit saves more time across a Quant section than any other fraction technique.

Adding needs a common denominator

Half a cake plus a third of a cake is hard to picture because the slices are different sizes. Cut both into sixths and it becomes 3 + 2 = 5 sixths.

There are always several common denominators available. Multiplying the two denominators together always works, and it is the fastest thing to reach for when the smallest one is not obvious.

Dividing means flipping

To divide by a fraction, take its reciprocal, the same fraction turned upside down, and multiply. A whole number becomes a fraction the same way: 5 is 5/1, so multiplying a fraction by 5 only affects the numerator.

Check that your answer makes sense

Four fifths of two thirds should come out near half a cake. It gives 8/15, and 8 is a bit more than half of 15. That check takes two seconds and catches errors before they cost you a question.