How To Multiply A Fraction And A Whole Number

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.

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.

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 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.