PRODUCT OF FRACTIONS
Product of Two Proper Fractions
The common word terms for multiply (x) are multiple of, of, product of
Method
Step1: Look for common factors
in numerator and denominator.
Reduce the values by the common factor
Step2: Multiply the numerator
Step3: Multiply the denominator
Product of a Fraction and a
Whole Number
Step1: Write whole number as Fraction with
denominator as 1
Step2: Look for common factors in numerator and
denominator.
Reduce the values by the
common factor
Step3: Multiply the numerator
Step4: Multiply the denominator
Product of a Mixed Number and a Whole Number
Method
Step1: Change the mixed number to an improper
function
Step2: Look for common factors in numerator and denominator.
Reduce the values by the
common factor
Step3:
Multiply the numerator
Step4: Multiply the denominator
Example:
Product of an Improper Fraction and a Proper fraction
Example
3 x 5 = 3 x 5
2 8 2 x 8
= 15
16
Product of a Mixed Number and an improper Fraction
=
7 x 6
5
5
= 42 (to convert to mixed number)
25
= 1 17
25
DIVISION OF
FRACTIONS
Recap: Multiplication
3
x 5 = 15 = 1 or
3 x 5
= 1
5 3
15 5 3
< Multiplying by the
“inverse” of the fraction itself =
1 >
Practice:
4 x 9 = 1 ☐ x 7 = 1 ☐x 3 = 1
☐ x 5 = 1
☐ ☐ ☐ 2 3 11 5 6
Solutions:
4 x 9 = 1 2 x 7
= 1 11 x 3 = 1
6 x 5
= 1
9
4 7 2 3 11 5 6
Linking
to Fraction Division
Example 2 ÷
5
3 7
= 2 x 7 ÷ 5
x 7 < multiply both fractions by “inverse” of
3 5
7 5 <optional : to explain why invert the
2nd number >
= 2 x 7 ÷
1
3 5
= 14
15
Method
Example 1 ÷ 3
5 4
Step1 1st fraction stays, change ÷
to x
1 x
5
Step 2 Inverse 2nd fraction
1 x 4
5 3
Step3 Solve
1 x 4
5 x 3
= 4
15
Dividing a Proper
Fraction by a Whole Number
Step1: Frist number stays, Change ÷ to x
Step2: Invert the divisor
Step3: Solve
Example
Example
Albert had 5/6l of milk. He split it equally into cups. Each cup contained 1/12l of milk. How many cups did Albert use?
Step 1: Keywords/Method?
- Circle Number, underline keywords
[student to understand 5/6l is a quantity (5/6) l (litre), not fraction 5/6 ]
{Draw Working}
[‘Split equally’ => divide, 5/6l , 1/12 l => fractions divide]
Step 2: Use fraction Division Method
a ÷ c = a x d
b d b c
5 ÷ 1 = 5 x 12 2
6 12 = 6 1
= 5 x 2
= 10
Step 3: Answer the question
[How many cups did Albert use?]
Albert used 10 cups.
Example of solving Fraction division Word Problems
Revise/Refresh:
➗ 100
|
Fractions
|
Decimals
|
8 ÷ 100 = 8 / 100
|
2/25
|
0.08
|
25 ÷ 100 = 25 / 100
|
1/4
|
0.25
|
30 ÷ 100 = 30 / 100
|
3/10
|
0.3
|
50 ÷ 100 = 30 / 100
|
1/2
|
0.5
|
62.5 ÷ 100 = 625 / 1000
|
5/8
|
0.625
|
75 ÷ 100 = 75 / 100
|
3/4
|
0.75
|
80 ÷ 100 = 80 / 100
|
4/5
|
0.8
|
97.5 ÷ 100 = 975 / 1000
|
39/40
|
0.975
|
