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Measurement. 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?.

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measurement

Measurement

Multiplying Fractions by Whole Numbers

multiplying fractions 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 numbers1
Multiplying Fractions & Whole Numbers
  • We can use several strategies to solve this problem:

5 x ¾ =

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

= 15/4 or 3 ¾

multiplying and dividing fractions
Multiplying and Dividing Fractions
  • Or, we can use a number line.

1

2

3

4

5

0

1

2

3

4

Answer: 5 x ¾ = 15/4 or 3 ¾

multiplying fractions whole numbers2
Multiplying Fractions & Whole Numbers
  • Another option: We can change the whole number to a fraction and multiply:

3

4

?

?

5

x

=

multiplying fractions whole numbers3
Multiplying Fractions & Whole Numbers
  • We can change the whole number to a fraction and multiply:

5

1

3

4

?

?

x

=

multiplying fractions whole numbers4
Multiplying Fractions & Whole Numbers
  • We can now multiply the fraction:

5

1

3

4

?

?

x

=

multiplying fractions whole numbers5
Multiplying Fractions & Whole Numbers
  • The answer is in fraction form.

5

1

3

4

15

4

x

=

multiplying fractions whole numbers6
Multiplying Fractions & Whole Numbers
  • This can be transformed into a mixed number.

5

1

3

4

3 ¾

x

=

multiplying fractions whole numbers7
Multiplying Fractions & Whole Numbers
  • Or, we can use the following process to multiply directly:
  • Multiply the whole number by the numerator

=

x

3

4

?

?

5

x

=

multiplying fractions whole numbers8
Multiplying Fractions & Whole Numbers
  • The answer is the new numerator.

=

x

3

4

15

?

5

x

=

multiplying fractions whole numbers9
Multiplying Fractions & Whole Numbers
  • The denominator remains the same as the denominator of the fraction.

3

4

15

?

5

x

=

multiplying fractions whole numbers10
Multiplying Fractions & Whole Numbers
  • This gives the answer in a fraction form.

3

4

15

4

5

x

=

multiplying fractions whole numbers11
Multiplying Fractions & Whole Numbers
  • This gives the answer in a fraction form.

3

4

15

4

5

x

=

multiplying fractions whole numbers12
Multiplying Fractions & Whole Numbers
  • This can then be transformed into a mixed number.

3

4

5

3 ¾

x

=

multiplying fractions whole numbers13
Multiplying Fractions & Whole Numbers
  • Assignment:

Page 100, Questions 1, 2, 3, 4