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Operations with Fractions Study Guide (page 2)

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Updated on Oct 3, 2011

Multiplying Fractions

To multiply fractions, multiply the numerators, then multiply the denominators, and finally simplify, if possible and necessary.

Try this with . First, multiply the numerators: 4 × 2 = 8. Now, do the same with the denominators: 5 × 3 = 15. So, >, which cannot be simplified.

Tip:

If you are asked to find the fraction of a number, multiply that number by the fraction. In other words, of means ×, or "multiply." For example, of 16 means .

Dividing Fractions

To divide one fraction by another, you need to flip the second fraction and then multiply the fractions. This flip of the second fraction is called the multiplicative inverse of a number or the reciprocal.

It's easier than it may seem. Try this problem:

First, find the reciprocal of. Now, multiply: .

Comparing Fractions

Sometimes, you may need to find the greatest fractions or put fractions in order from least to greatest or from greatest to least.

Let's try putting the following fractions from least to greatest:

To do this, you should first give all the fractions a common denominator. The least common multiple of 3 and 4 is 12, so let's make 12 the new denominator for all four fractions:

All that's left to do is to put the numbers in order from least to greatest:

So, this means the order of the fractions from least to greatest would be and .

Find practice problems for these concepts at Operations with Fractions Practice Questions.

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