- 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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# Division Involving a Whole Number and a Fraction

The division involving a whole number and a fraction is done as follows.

**Rules of division**

The whole number, at first, is written as a fraction. The division then becomes division of two fractions.

Dividing by a number is same as multiplying with its reciprocal.

The multiplication of the fractions follows the same procedure as learnt in previous lessons.

The numerators across the top are multiplied; the denominators across the bottom are multiplied.

If required, the resulting fraction is simplified.

Divide $\frac{7}{6}$ ÷ 3

### Solution

**Step 1:**

Re-writing

$\frac{7}{6}$ ÷ 3 = $\frac{7}{6}$ ÷ $\frac{3}{1}$

**Step 2:**

As dividing by a number is same as multiplying by its reciprocal

$\frac{7}{6}$ ÷ $\frac{3}{1}$ = $\frac{7}{6}$ × $\frac{1}{3}$ = $\frac{7}{18}$

**Step 3:**

So, $\frac{7}{6}$ ÷ 3 = $\frac{7}{18}$

Divide 6 ÷ $\frac{5}{7}$

### Solution

**Step 1:**

Re-writing

6 ÷ $\frac{5}{7}$ = $\frac{6}{1}$ ÷ $\frac{5}{7}$

**Step 2:**

As dividing by a number is same as multiplying by its reciprocal

$\frac{6}{1}$ ÷ $\frac{5}{7}$ = $\frac{6}{1}$ × $\frac{7}{5}$ = $\frac{(6×7)}{(1×5)}$ = $\frac{42}{5}$

**Step 3:**

So, 6 ÷ $\frac{5}{7}$ = $\frac{42}{5}$