Compare Fractions

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Suppose that you made a cake, and you want to give  of the cake to your friend, but then you learn that your friend took  of the cake. So, did your friend take more, less, or the exact amount that you wanted to give him? 

We can draw both fractions:

 

 

By looking at the figure, both fractions appear to be the same, but is this the case? We need a better way to compare these fractions.

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Question

Compare and .

Solution

There are two ways to compare these fractions:

I.  Find a Common Denominator

To find the answer, we can compare the numerators for both fractions by converting their denominators to the same value.

First, multiply the values on one side by the denominator on the opposite side:

?

?

Now that both denominators are the same, compare numerators:

  ?

From here we can see that ²¹/₃₅ > ²⁰/₃₅ since 21 > 20, and so:

>

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II.  Convert Fractions to Decimals

You can also compare the fractions by dividing the numerator by the denominator.

?

3 ÷ 5  ?  4 ÷ 7

Compare both values

0.6 > 0.571428

Either way, you know now that your friend did not take as much cake as you wanted to give him.

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Try it yourself

Order the following fractions from least to greatest.

1.) 

2.)

3.) 1 3

Insert <, > or = to make to the following statements true.

4.)  ___ 

5.)  2 ___ 3

6.)  ___ 3

7.)  ___

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Answer Key