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# Multiplying a Fraction by an Integer

A fraction is a way of expressing division. For example, the fraction $\frac{4}{8}$ is equivalent to $4÷8$ . The number above the bar of a fraction is the numerator, and the number below the bar is the denominator.

Integers are the set of whole numbers (ex. 2, 17, and 398) and their opposites (ex. -4, -25, -99). Decimals (ex. 0.32), fractions (ex. 34), and mixed numbers (ex. $5\frac{17}{18}$ ) are not integers.

## How to multiply a fraction by an integer

So, how do you multiply a fraction by an integer? A way to think about it is to remember that multiplication is repeated addition.

For example, if you want to multiply $5×\frac{1}{11}$ , you can write the multiplication as an addition by adding $\frac{1}{11}$ five times:

$5×\frac{1}{11}=\frac{1}{11}+\frac{1}{11}+\frac{1}{11}+\frac{1}{11}+\frac{1}{11}$

Now, add fractions with like denominators. You'll keep the denominator the same and add the numerators:

$\frac{1+1+1+1+1}{11}$

Answer: $\frac{5}{11}$

Another way to multiply a fraction by an integer is to rewrite the whole number as a fraction:

$3\cdot \frac{2}{7}=\frac{3}{1}\cdot \frac{2}{7}$

Next, multiply the numerators and denominators using the rules for multiplying fractions:

$3\cdot \frac{2}{1}\cdot 7$

Answer: $\frac{6}{7}$

Keep in mind that you might sometimes need to reduce the fraction to get the simplest form or lowest terms:

$2\cdot \frac{5}{8}=\frac{10}{8}$

In this case, both the numerator and denominator have a common factor of 2. Divide both by 2:

$\frac{10}{8}=\frac{5}{4}$

You could also get an answer greater than one and need to rewrite the improper fraction as a mixed number:

$\frac{5}{4}$

Answer: $1\frac{1}{4}$

## Practice questions on multiplying a fraction by an integer

Multiply each fraction by the integer:

a. $2\cdot \frac{2}{9}$

Answer: $\frac{4}{9}$

b. $6\cdot \frac{1}{8}$

Answer: $\frac{6}{8}=\frac{3}{4}$

c. $8\cdot \frac{3}{4}$

Answer: $\frac{24}{4}=6$

d. $4\cdot \frac{3}{18}$

Answer: $\frac{12}{18}=\frac{2}{3}$

e. $9\cdot \frac{1}{6}$

Answer: $\frac{9}{6}=\frac{3}{2}$

f. $7\cdot \frac{7}{13}$

Answer: $\frac{49}{13}$

## Get help learning about multiplying a fraction by an integer

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