# Multiplying a Fraction by an Integer

A fraction is a way of expressing division. For example, the fraction $\frac{4}{8}$ is equivalent to $4\xf78$ . 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 $5\times \frac{1}{11}$ , you can write the multiplication as an addition by adding $\frac{1}{11}$ five times:

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

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: $\frac{49}{13}$

## Topics related to the Multiplying a Fraction by an Integer

## Flashcards covering the Multiplying a Fraction by an Integer

Common Core: 4th Grade Math Flashcards

## Practice tests covering the Multiplying a Fraction by an Integer

Common Core: 4th Grade Math Diagnostic Tests

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

Ensuring that your student understands how to multiply a fraction by an integer can help set a foundation that will make solving math problems easier as they become more complex. If your student is having trouble solving these types of problems on homework assignments or would like to refresh their knowledge while preparing for a test, working with a tutor can help. It can be difficult to find your student a qualified math tutor on your own, so let Varsity Tutors help. Learn all about the perks of tutoring by reaching out to the Educational Directors at Varsity Tutors.

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