How to Tell Which Fraction is Largest

The secret is to cross-multiply the two fractions. Cross-multiplication is a handy math skill to know. You can use it for a quite few different purposes. You are going to use it to find out which of two fractions is greater.

To cross-multiply two fractions:

1. Multiply the numerator of the first fraction by the denominator of the second fraction and jot down the answer.
2. Multiply the numerator of the second fraction by the denominator of the first fraction and jot down the answer.

For example, suppose you have these two fractions:

 3              4

---  and    ---

 7              9

When you cross-multiply, you get these two numbers: 3 X 9 = 27 and 4 X 7  = 28

Make sure you start with the numerator of the first fraction. To find out which of two fractions is larger, place the two numbers you get, in order, under the two fractions. The larger number is always under the larger fraction.

 3              4

---            ---

 7              9

27            28

so 4/9 is larger than 3/7 (or 4/9 > 3/7).

What do you do if you have more than 2 fractions?

Answer: You take them two at a time.

For example, we have the fractions 5/13, 7/17, and 8/19. Which is the largest?

Take the first two and cross multiply:

 5                                7

---             and           ---

13                              17

5 X 17 = 85               7 X 13 = 91

so 7/17 is larger than 5/13.

Now take the larger of these two, 7/17 and compare it with the third, 8/19.  

 7                                8

---             and           ---

17                              19

7 X 19=133              8 X 17=136

so 8/19 is larger than 7/17 is larger than 5/13.