- 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

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
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- Who is Who

# Introduction to Fraction Multiplication

The product of two fractions is obtained by multiplying the numerators and then multiplying the denominators of the fractions to get the product fraction. If any simplification or cross cancelling is required, it is done and fraction is written 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.
- If required, we simplify the fraction so obtained and reduce it to the lowest terms.

**Example**

Multiply $\frac{2}{3}$ × $\frac{5}{7}$

**Solution**

**Step 1:**

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{2}{3}$ × $\frac{5}{7}$ = $\frac{(2 × 5)}{(3 × 7)}$ = $\frac{10}{21}$

**Step 2:**

Since no number other than 1 evenly divides both 10 and 21, this is the answer in simplest form.

$\frac{2}{3}$ × $\frac{5}{7}$ = $\frac{10}{21}$

Multiply $\frac{2}{7}$ × $\frac{9}{5}$

### Solution

**Step 1:**

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{2}{7}$ × $\frac{9}{5}$ = $\frac{(2 × 9)}{(7 × 5)}$ = $\frac{18}{35}$

**Step 2:**

Since no number other than 1 evenly divides both 18 and 35, this is the answer in simplest form.

$\frac{2}{7}$ × $\frac{9}{5}$ = $\frac{18}{35}$

Multiply $\frac{4}{5}$ × $\frac{8}{9}$

### Solution

**Step 1:**

We multiply the numerators on the top and denominators on the bottom as follows.

$\frac{4}{5}$ × $\frac{8}{9}$ = 4 × $\frac{8}{(5 × 9)}$ = $\frac{32}{45}$

**Step 2:**

Since no number other than 1 evenly divides both 32 and 45, this is the answer in simplest form.

$\frac{4}{5}$ × $\frac{8}{9}$ = $\frac{32}{45}$