- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division
Multiplication of 3 Fractions
The product of three fractions is obtained by multiplying the numerators and then multiplying the denominators of the three fractions to get the product fraction. If any simplification or cross cancelling is required, it is done and fraction obtained is in lowest terms. The following three steps are followed in fraction multiplication.
- We multiply the top numbers or numerators
- We multiply the bottom numbers or denominators
- We simplify the fraction so obtained if required
Example
Multiply $\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$
Solution
Step 1:
We multiply the numerators at the top and denominators at the bottom of all three fractions as follows.
$\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$
= $\frac{(2 × 5 × 8)}{(3 × 7 × 9)}$ = $\frac{80}{189}$
Step 2:
The highest common factor of 80 and 189 is 1
So, $\frac{2}{3}$ × $\frac{5}{7}$ × $\frac{8}{9}$ = $\frac{80}{189}$
Multiply $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$
Solution
Step 1:
First Multiply $\frac{2}{5}$ × $\frac{15}{8}$
Multiply the numerators and denominators of both fractions as follows.
$\frac{2}{5}$ × $\frac{15}{8}$ = $\frac{(2 × 15)}{(5 × 8)}$ = $\frac{30}{40}$
Step 2:
Simplifying
$\frac{30}{40}$ = $\frac{3}{4}$
So $\frac{2}{5}$ × $\frac{15}{8}$ = $\frac{3}{4}$
Step 3:
Now $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$ = $\frac{3}{4}$ × $\frac{4}{5}$ = $\frac{3}{5}$.
So, $\frac{2}{5}$ × $\frac{15}{8}$ × $\frac{4}{5}$ = $\frac{2}{5}$.
Multiply $\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$
Solution
Step 1:
Multiply the numerators at the top and denominators at the bottom of all three fractions as follows.
$\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$
= $\frac{(3 × 8 × 5)}{(4 × 9 × 7)}$ = $\frac{120}{252}$
Step 2:
The highest common factor of 120 and 252 is 12
$\frac{(120÷12)}{(252÷12)}$ = $\frac{10}{21}$
Step 3:
So, $\frac{3}{4}$ × $\frac{8}{9}$ × $\frac{5}{7}$ = $\frac{10}{21}$
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