How to Multiply and Divide Fractions

By eHow Contributor
Both 1/4 and 1/2 are simple fractions that represent different mathematical data.
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Elementary school children learn about multiplying and dividing fractions in math class. Success depends on following a few simple rules and understanding what the numbers in fractions signify. The number above the line in a fraction is the numerator, while the number beneath is the denominator. Imagine a pizza at the center of the dinner table. Your numerator is the number of slices you have on your plate, while the denominator is the total number of slices that made up a whole pizza. So if you remove three slices out of eight, you have had three-eighths of the pizza.

Step 1

Multiply your numerators together when you're multiplying fractions. The product is the numerator of the answer. Multiply the denominators together to get the denominator of the answer. Consider the problem of 2/3 x 2/5. Multiply your numerators: 2 x 2 = 4. Then multiply your denominators: 3 x 5 = 15. So the final answer is 4/15.

Step 2

Convert your whole number into a fraction with 1 as its denominator when you multiply a fraction by a whole number. For example, consider 2/3 x 4. Convert 4 into 4/1 The equation now looks like 2/3 x 4/1. Multiply the numerators: 2 x 4 = 8; multiply the denominators: 3 x 1 = 3. Your answer is 8/3. You can convert this improper fraction into a mixed fraction by dividing 8 by 3, which equals 2 2/3.

Step 3

Remember one simple rule when dividing fractions: Turn your second fraction upside down and multiply, following the previous steps. For example, suppose you have (1/5) / (5/8). Invert the second fraction and multiply. So your equation becomes: (1/5) * (8/5). Multiply your numerators: 1 x 8 = 8; multiply your denominators: 5 x 5 = 25. Your answer is 8/25

When dividing by whole numbers, remember to convert your whole number into a fraction by using the whole number as the numerator and using a 1 as the denominator.

Step 4

Simplify your result whenever possible. For instance, if you multiply 3/4 by 8/9, your answer will be 24/36. Divide both the numerator and denominator by the greatest common factor. In this case, that's 12. So the final result becomes 2/3.