SEARCH HOME
 Math Central Quandaries & Queries
 Question from Melissa, a student: Hello i am a sixth grader, On my homework sheet there is the question : 5/45 _ 9/81 But it says to Compare the fractions. Use <,>, or = and i find it difficult to answer, please help me find a simple way to answer questions like this.

We have two responses for you

Hi Melissa,

To compare two fractions easily you need them to have the same denominator. For example suppose the fractions are 5/21 and 7/18. Find the prime factorization of 21 and 18

21 = 3 × 7
18 = 2 × 3 × 3

The smallest number that is a multiple of 21 and 18 is 3 × 7 × 2 × 3 = 126,

126 = 21 × 6 and 126 = 18 × 7.

Thus

5/21 = (5 × 6)/(21 × 6) = 30/126 and
7/18 = (7 × 7)/(18 × 7) = 49/126

Thus 7/18 > 5/21.

I hope this helps,
Penny

Hi Melissa.

If you are comparing positive fractions, the easiest thing to do is to "cross-multiply".

Here is an example: 10/17 ? 3/5 (replace the question mark with <, =, or > )

I multiply both sides of this equation by the denominators:

10/17 x 17 x 5 ? 3/5 x 17 x 5

Now I cancel on each side with the denominator:

10 x 5 ? 3 x 17

(you can skip straight to this step if you want - that's a shortcut). Now just multiply it out:

50 ? 51

Definitely the answer here is < (less than) because 50 < 51. That means the original question is also <.

10/17 < 3/5.

Try it with your numbers. It will be easiest if you first "simplify" each of your fractions, then you are working with smaller numbers. When you simplify first, you may find the answer is obvious to you!

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.