How to Multiply a Fraction and a Whole Number

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Whether you're drilling this skill or solving a word problem, there are several steps to follow when multiplying a fraction and a whole number. If you are solving a word problem, the word "of" in math translates to multiplication. If you have to find "three-eighths of 32 people," your equation to solve it is 3/8 x 32.

Whole Number as a Fraction

The first step to multiplying a whole number by a fraction is to turn it into a fraction itself. A fraction is really a division problem, and every number is divisible by 1. To turn a whole number into a fraction without changing its value, put it over a denominator of 1. This is true for any number, no matter the size. One million as a fraction is 1,000,000/1. To find 3/8 of 32 people, your problem becomes 3/8 x 32/1.

Multiply the Numerators

Once you have turned your whole number into a fraction, follow the rules for multiplying fractions. Multiply the top numbers of the fraction, straight across. The top numbers are the numerators. For example, with 3/8 x 32/1, multiply 3 x 32 to get 96. The numerator of your answer is 96.

Multiply the Denominators

Multiply the numbers on the bottoms of the fractions, called the denominators. This is simple if you are multiplying by a whole number, because the denominator of the whole number is 1. For 3/8 x 32/1, multiply 8 x 1. The product of your denominators is the denominator of your answer: 8.


Your answer is not complete until you have written your product in its simplest form. To simplify a fraction, divide the numerator and the denominator by the greatest common factor, which is the biggest number that goes into both evenly. In the example of finding 3/8 of 32 people, your initial answer is 96/8, but this is not in its simplest form. Both 96 and 8 are divisible by 2, 4 and 8, with 8 being the greatest common factor. Divide the numerator and the denominator by 8 to get 12/1, or 12. Your answer is 12 people.


About the Author

Hannah Richardson has a Master's degree in Special Education from Vanderbilt University and a Bacheor of Arts in English. She has been a writer since 2004 and wrote regularly for the sports and features sections of "The Technician" newspaper, as well as "Coastwach" magazine. Richardson also served as the co-editor-in-chief of "Windhover," an award-winning literary and arts magazine. She is currently teaching at a middle school.

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