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Multiplying Fractions by
Whole Numbers
Multiplying Fractions &
Whole Numbers
 Many problems require the
multiplication of whole numbers by a
fraction.
Example: Five packages of
cookies are each ¾ full.
How many full packages would
this be if they were combined?
Multiplying Fractions &
Whole Numbers
 We can use several strategies to solve this
problem:
5x¾=
By counting the number of quarters (1/4) blocks
colored, we can determine the answer.
= 15/4 or 3 ¾
Multiplying and Dividing
Fractions
 Or, we can use a number line.
1
0
2
1
3
4
2
5
3
4
Answer: 5 x ¾ = 15/4 or 3 ¾
Multiplying Fractions &
Whole Numbers
 Another option: We can change the
whole number to a fraction and
multiply:
5
x
3
4
=
?
?
Multiplying Fractions &
Whole Numbers
 We can change the whole number to
a fraction and multiply:
5
1
x
3
4
=
?
?
Multiplying Fractions &
Whole Numbers
 We can now multiply the fraction:
5
1
x
3
4
=
?
?
Multiplying Fractions &
Whole Numbers
 The answer is in fraction form.
5
1
x
3
4
=
15
4
Multiplying Fractions &
Whole Numbers
 This can be transformed into a mixed
number.
5
1
x
3
4
=
3 ¾
Multiplying Fractions &
Whole Numbers
 Or, we can use the following process
to multiply directly:
 Multiply the whole number by the
numerator
=
x
5
x
3
4
=
?
?
Multiplying Fractions &
Whole Numbers
 The answer is the new numerator.
=
x
5
x
3
4
=
15
?
Multiplying Fractions &
Whole Numbers
 The denominator remains the same
as the denominator of the fraction.
5
x
3
4
=
15
?
Multiplying Fractions &
Whole Numbers
 This gives the answer in a fraction
form.
5
x
3
4
=
15
4
Multiplying Fractions &
Whole Numbers
 This gives the answer in a fraction
form.
5
x
3
4
=
15
4
Multiplying Fractions &
Whole Numbers
 This can then be transformed into a
mixed number.
5
x
3
4
=
3¾