Multiplying fractions and whole numbers

Multiplying fractions and whole numbers

How do you multiply a fraction by a whole number?

• You can follow these steps to multiply a fraction by a whole number

• Step 1: Write the whole number as a fraction with a denominator of 1.

• Step 2: Multiply the numerators.

• Step 3: Multiply the denominators.

• Step 4: Simplify, if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.

Let's try it! 1st Step!

You will need your whiteboards!
Write your problem down!

First, write the whole number as a fraction with a denominator of 1.

Since 3 is our whole number, we will write the fraction  $\frac{3}{1}$  

3 =  $\frac{3}{1}$  

2nd Step!

Now, multiply the numerators and the denominators.  $\frac{2}{5}$  x  $\frac{3}{1}$  

2 x 3 = ?
5 x 1 = ?

3rd Step

Last, simplify. Since  $\frac{6}{5}$  is greater than 1, change it to a mixed number.

You got it!

So  $\frac{2}{5}$  x  $3$   =  $1\ \frac{1}{5}$  

Multiple Choice

 $\frac{1}{5}$  x  $5$  

•  $\frac{5}{5}$  

• 1

•  $\frac{6}{5}$  

•  $1\ \frac{1}{5}$  

Multiple Choice

 $8\times\frac{1}{2}$  

•  $\frac{8}{2}$  

•  $\frac{9}{2}$  

• 4

•  $4\ \frac{1}{2}$  

Multiple Choice

 $9\times\frac{1}{2}$  

•  $\frac{10}{2}$  

•  $\frac{9}{2}$  

•  $4\ \frac{1}{3}$  

•  $4\ \frac{1}{2}$  

Multiple Choice

 $\frac{3}{8}\times7$  

•  $2\ \frac{5}{8}$  

•  $\frac{21}{8}$  

•  $\frac{10}{8}$  

•  $1\ \frac{2}{8}$  

Why does this work?

When you multiply a fraction by a whole number, you can think of the problem as repeated addition.

Look at the problem  $\frac{2}{5}\times3$ . That's the same as  $\frac{2}{5}+\frac{2}{5}+\frac{2}{5}$ .

Remember!

 $\frac{2}{5}\times\frac{3}{1}=\frac{2\times3}{5\times1}=\frac{6}{5}=1\ \frac{1}{5}$  

A fraction of a whole number

Let's say there are 8 apples in a basket, and  $\frac{1}{2}$  of those apples are red. How many of the apples are red?

Fraction of a whole number

Finding  $\frac{1}{2}$  of  $8$  is the same as multiplying  $\frac{1}{2}\times8$ . Follow the steps we have learned to solve!

Solve on your whiteboards!

What is  $\frac{1}{2}$  of  $8$ ?

The answer...

So, 4 of the apples are red.

IXL Practice

Skill Code: JLH

Skill Code: QB8