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# Comparing Fractions

As mathematicians, we often find ourselves working with fractions. Although this might sound a little complicated at first, we can compare these fractions easily in just a few steps. Follow this guide, and you''ll learn how to find out which fraction is greater.

## A quick review of terminology

Understanding basic terminology is important when working with fractions. The numerator represents the number of parts we have, while the denominator represents the total number of parts in the whole. For example, in the fraction

3/5
, the numerator is 3 and the denominator is 5. A common denominator is important when adding or subtracting fractions with different denominators. To find a common denominator, we need to find a multiple that both denominators share. The smallest common denominator is the least common multiple of the two denominators, which we can find by listing the multiples of each denominator and finding the smallest number that appears on both lists. Alternatively, we can also find a common denominator by multiplying the two denominators together, but this is not always the smallest common denominator.

## How to Compare Fractions

Which fraction has the largest value,

4/7 or 7/11?
At first glance, it might be difficult to answer with absolute certainty. Both are slightly more than
1/2
.

To find out, let''s find a common denominator. We''ll use 77, since:
7*11 = 77.

If we multiply:
4/7 * 11/11

and
7/11 * 7/7
we will get them both over the same common denominator:

4/7 =(4*11)/(7*11) = 44/77

7/11 = 7*7/11*7 = 49/77

Now we can see that
49/77 > 44/77
So that must also mean that
7/11 > 4/7

## Topics related to the Comparing Fractions

Converting Fractions to Decimals

Equivalent Fractions

Fractions

## Flashcards covering the Comparing Fractions

Basic Arithmetic Flashcards

## Practice tests covering the Comparing Fractions

Common Core: 3rd Grade Math Diagnostic Tests