Multiplying Fractions

Simplify your multiplication by dividing it into steps.
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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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