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Fraction Operations Lessons

Comparing Any Fractions: Learn

If two fractions have different numerators and denominators it is difficult to determine which fraction is larger. It is easier to determine which is larger if both fractions have the same denominator. This same denominator is often referred to as a common denominator.

To find this common denominator, multiply each fraction as necessary to produce equivalent fractions. For example, if you are comparing

5
12
   and  
1
3

Then 1/3 should be multiplied by 4/4. It does not change the value of 1/3 to be multiplied by 4/4 (which is equal to 1) because any number multiplied by 1 is still the same number. After the multiplication (1/3 * 4/4 = 4/12), the comparison can be made between 5/12 and 4/12.

5
12
   is larger than  
1 * 4 =
3 * 4 =
4
12

You may have to multiply both fractions by different numbers to produce the same denominator for both fractions. For example, if you are comparing

2
3
   and  
3
4

Then we need to multiply 2/3 by 4/4 to give 8/12 and multiply 3/4 by 3/3 to give 9/12. The fraction 3/4 which is equal to 9/12 is larger than 2/3 which is equal to 8/12.

2 *4 =
3 * 4 =
8
12
   is less than  
3 * 3 =
4 * 3 =
9
12

Compare Like Fractions: Practice

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