- 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

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# Fraction Multiplication

### Rules for fraction multiplication

To get the product of two fractions

- We multiply the numerators.
- We multiply the denominators.
- If required, we cross cancel or simplify before multiplying.
- In such a case, we get a fraction in lowest terms.

**Example**

Multiply $\frac{4}{5}$ × $\frac{7}{9}$

### Solution

**Step 1:**

Multiply the numerators and denominators of both fractions as follows.

$\frac{4}{5}$ × $\frac{7}{9}$ = $\frac{(4 × 7)}{(5 × 9)}$ = $\frac{28}{45}$

**Step 2:**

So, $\frac{4}{5}$ × $\frac{7}{9}$ = $\frac{28}{45}$

Multiply $\frac{4}{5}$ × $\frac{10}{16}$ and write the answer as a fraction in simplest form

### Solution

**Step 1:**

We multiply the numerators and denominators of both fractions as follows.

$\frac{4}{5}$ × $\frac{10}{16}$ = $\frac{(4 × 10)}{(5 × 16)}$ = $\frac{40}{80}$

**Step 2:**

Dividing numerator and denominator with the gcf of 40 and 80 which is 40.

So, $\frac{40÷40}{80÷40}$ = $\frac{1}{2}$

**Step 3:**

$\frac{4}{5}$ × $\frac{10}{16}$ = $\frac{1}{2}$

This is the answer as a fraction in simplest form.

Multiply $\frac{3}{4}$ × $\frac{12}{15}$ and write the answer as a fraction in simplest form

### Solution

**Step 1:**

We cross cancel 3 and 15 diagonally; we also cross cancel 4 and 12 diagonally.

$\frac{3}{4}$ × $\frac{12}{15}$ = $\frac{1}{1}$ × $\frac{3}{5}$

**Step 2:**

We multiply the numerators. Then we multiply the denominators.

$\frac{1}{1}$ × $\frac{3}{5}$ = $\frac{(1 × 3)}{(1 × 5)}$ = $\frac{3}{5}$

**Step 3:**

So $\frac{3}{4}$ × $\frac{12}{15}$= $\frac{3}{5}$

This is already in simplest form.