Separating the process of multiplying fractions into a few smaller steps will help you better understand the process. Remember that fractions are made up of two parts: the *numerator* on top and the *denominator* on the bottom. In fraction multiplication, numerators and denominators are multiplied individually to produce the final fraction.

## Multiplying Two Fractions

To multiply two fractions, you **multiply the numerators by each other, and multiply the denominators by each other.** The product of the two numerators is your answer's numerator, and the product of the two denominators is the answer's denominator. Take the following:

3/5 x 2/3

First, multiply the numerators: 3 x 2 = 6. Then multiply the denominators: 5 x 3 = 15. Construct the multiplied fraction with the new numerator on top and the new denominator on the bottom:

3/5 x 2/3 = 6/15

## Simplifying Fractions

After you multiply fractions together, check if you can *simplify* the answer. You can simplify a fraction if both the numerator and the denominator can be divided by the same number. You can simplify 6/15 because both 6 and 15 are divisible evenly by 3: 6 / 3 = 2 and 15 / 3 = 5. Your simplified answer is 2/5. You can't divide 2 and 5 further, so you cannot further simplify the fraction:

3/5 x 2/3 = 6/15 = 2/5

Note that if the denominator evenly divides into the numerator, the simplified fraction is a whole number. For example:

4/3 x 6/4 = 24/12 = 2/1 = 2

## Multiplying Fractions by Whole Numbers

A whole number, like 5, can be expressed as a fraction with the whole number as the numerator and 1 as the denominator:

5 = 5/1

You can multiply any fraction by a whole number simply by **multiplying the numerator by the whole number.** For example, take 4 x 5/12. Multiply 4 by 5 to produce the new numerator, 20. The denominator stays the same:

4 x 5/12 = 4/1 x 5/12 = 20/12

Check if you can simplify this fraction; you can, both 20 and 12 are divisible by 4. Divide both by 4, to get 5/3. You cannot divide 5/3 further, so you have your answer:

4 x 5/12 = 20/12 = 5/3

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