Multiplying a Fraction by a Whole Number
Suppose we want to multiply the fraction  by the number 3. We can
think of multiplying the fraction by 3 as taking “3 copies
of ”. We can model
this multiplication by drawing a rectangle, dividing it into 8
equal pieces, and then shading 3 of them.
The shaded pieces represent  of the entire
rectangle. Notice that this answer can be found by multiplying
the numerator of the fraction by 3 and retaining the
denominator.
Key Idea
To multiply a fraction by a whole number, multiply the
numerator in the fraction by the whole number and place this
product over the denominator.
Example 1
Example 2
Example 3
Why Does This Procedure Work?
The multiplication of two whole numbers can be thought of as
repeated addition. For example,
| 2 × 3 = 3 + 3 |
3 × 7 = 7 + 7 + 7 |
5 × 9 = 9 + 9 + 9 + 9 + 9 |
The multiplication of a fraction by a whole number can be
thought of in the same way.
When we add fractions with like denominators, we add them by
adding the numerators and retaining the denominator. The repeated
additions involve adding fractions with like denominators since
the fractions are the same.
The last step of the process in each example above shows that
multiplying a fraction by a whole number is accomplished by
multiplying the whole number times the numerator and keeping the
same denominator.
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