Measurement

Multiplying Fractions by Whole Numbers

Many problems require the multiplication of whole numbers by a fraction.

Multiplying Fractions & Whole Numbers

Example: Five packages of cookies are each ¾ full.

How many full packages would this be if they were combined?

We can use several strategies to solve this problem:

Multiplying Fractions & Whole Numbers

5 x ¾ =

= 15/4 or 3 ¾

By counting the number of quarters (1/4) blocks colored, we can determine the answer.

Or, we can use a number line.

Multiplying and Dividing Fractions

0 1 2 3 4

1 2 3 4 5

Answer: 5 x ¾ = 15/4 or 3 ¾

Another option: We can change the whole number to a fraction and multiply:

Multiplying Fractions & Whole Numbers

5 x34

??

=

We can change the whole number to a fraction and multiply:

Multiplying Fractions & Whole Numbers

x34

??

=51

We can now multiply the fraction:

Multiplying Fractions & Whole Numbers

x34

??

=51

The answer is in fraction form.

Multiplying Fractions & Whole Numbers

x34

154

=51

This can be transformed into a mixed number.

Multiplying Fractions & Whole Numbers

x34

3 ¾ =51

Or, we can use the following process to multiply directly:

Multiply the whole number by the numerator

Multiplying Fractions & Whole Numbers

5 x34

??

=

x =

The answer is the new numerator.

Multiplying Fractions & Whole Numbers

5 x34

15?

=

x =

The denominator remains the same as the denominator of the fraction.

Multiplying Fractions & Whole Numbers

5 x34

15?

=

This gives the answer in a fraction form.

Multiplying Fractions & Whole Numbers

5 x34

154

=

This gives the answer in a fraction form.

Multiplying Fractions & Whole Numbers

5 x34

154

=

This can then be transformed into a mixed number.

Multiplying Fractions & Whole Numbers

5 x34

3 ¾ =