How to Multiply Fractions With Mixed Numbers

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Before multiplying fractions, you convert any mixed numbers to improper fractions. You then multiply all the fractions in your problem, simplify if possible and finally convert back into mixed number form.

Convert Mixed to Improper

To convert a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. For example, in the fraction 5 3/8, multiply the denominator 8 and the whole number 5, then add the numerator 3:

(8 x 5) + 3 = 43

The answer becomes your new numerator. The denominator stays the same. In the example, the improper fraction is 43/8. Repeat this process for all mixed numbers in your equation.

Multiply the Fractions

Once you've converted all fractions to improper fraction form, multiply the fractions as you would in any fraction multiplication problem. First, multiply all the numerators. Then multiply all the denominators. Write the answers in fraction form with the numerator product on top and the denominator product on bottom. For the problem 10/3 x 3/4, multiply 10 and 3 to find the numerator of 30. Multiply 3 and 4 to find the denominator of 12. Your answer is 30/12.

Simplify the Answer

You might need to simplify your answer to its lowest terms. Simplifying at this point makes conversion back to a mixed number easier. Look at the numerator and denominator and determine if any number can divide into both of them. If they are both divisible by more than one number, look for the highest number. In 48/18, both numbers are divisible by 2, 3 and 6. Since 6 is the largest, divide both numbers by 6 to get 8/3.

Convert Back to Mixed Number

If your answer is an improper fraction, convert it back to a mixed number after simplifying. Instead of multiplying, this time you divide the top number by the bottom number. In the improper fraction 32/5, divide 32 by 5. Your answer is 6 plus a remainder of 2. The 6 becomes your whole number. The 2 becomes the numerator in the mixed number. Your denominator stays the same, so 32/5 becomes 6 2/5.


About the Author

Based in the Midwest, Shelley Frost has been writing parenting and education articles since 2007. Her experience comes from teaching, tutoring and managing educational after school programs. Frost worked in insurance and software testing before becoming a writer. She holds a Bachelor of Arts in elementary education with a reading endorsement.

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