### Key Concepts

• Use an area model to divide fractions

• Use another area model to divide fractions

• Divide fractions

**Introduction**:

## Dividing a fraction by another fraction:

Division of a fraction by another fraction is similar to the multiplication of a fraction by the reciprocal of the opposite fraction.

For instance, reciprocal of 2/5 is 5/2

**Example:** Divide 3/4 / 2/7

**Solution:**

The division of the given fractions can be performed with visual representation as shown,

**How to divide a fraction by a fraction?**

The following steps explains the fractions division:

Step 1: Write the fractions.

Step 2: Flip the divisor into reciprocal.

Step 3: Replace the division sign with multiplication sign.

Step 4: Multiply both the fractions’ numerators and denominators.

Step 5: Simplify the multiplication and the resultant product is the answer.

**Example:** Divide 1/2 / 1/4

**Solution: **

Given fractions are 1/2 and 1/4

Here, the divisor fraction is 1/4

Reciprocal of 1/4 is 4/1, flipping the divisor.

**1.5.1 Use an area model to divide fractions**

**What is an area model?**

An area model is a rectangular diagram used for multiplication and division problems.

**How can we use an area model to represent the division?**

Solving division problems using area models are explained with the help of the following example.

**Example 1: **Use an area model to divide the fractions 1/2 /÷ 1/6

**Solution:**

We can find the quotient for the given factions using an area model in two steps.

Step 1: First, draw an area model to represent the dividend 1/2

Now, find the number of 1/6 parts in 1/2

Step 2: Divide the area model into 1/6 parts to represent the divisor.

From the above figure, we can divide three 1/6 parts from 1/2

**Example 2:** Use an area model to divide 2/5 ÷ 1/10

**Solution:**

Given factions can be represented using the below area model

From the above figure, we can divide four 1/10 parts from 2/5

**1.5.2 ****Use another area model to divide fractions**

**Example 1:** Use fraction bars to divide 2/3 ÷ 3/4

**Solution: **

Step 1: Draw the fraction bars to represent 2/3 and 3/4

Step 2: Find the common unit by multiplying the fractions

2/3 can be divided into 8 equal parts.

3/4 can be divided into 9 equal parts.

**1.5.3 ****Divide fractions**

Division of a fraction by a fraction is performed by the reciprocal of the divisor.

**Example 1:** Divide 3/4 ÷ 1/6

**Solution:**

Rewriting the problem as a multiplication problem with the reciprocal of the divisor.

Reciprocal of 1/6 is 6/1

3/4÷1/6 = 3/4 × 6/1 = 18/4 or 9/2 or 4 1/2

or 9/2 or 4 1/2

**Example 2:** A swimming pool is in the rectangular shape with an area of 1/6 square yard. The width of the pool is 2/3 yard. Find the length of the swimming pool. Use the formula A = L × W.

**Solution: **

Given, area = 1/6 square yard

width = 2/3 yard

length = ?

From the above figure,

A = L × W

Rewriting the problem as a multiplication problem with the reciprocal of the divisor.

L = 3/12 or 1/4

Length of the swimming pool is 1/4 yard.

**Example 3:** Find the quotient of 2/5 ÷ 1/8

**Solution:**

Given 2/5 ÷ 1/8

Rewriting the problem as a multiplication problem with the reciprocal of the divisor.

Reciprocal of 1/8 is 8/1

## Exercise:

1. Find the quotient of 5/8 ÷ 1/2

2. Draw a diagram to find 3/4 ÷ 2/3

3. Write a division sentence to represent the below model diagram.

4. Find n in the equation 13/6 ÷1/6 = n

S. Use fraction bars to find 4/9 ÷ 2/3

6. Find the division sentence shown in the below model.

7. Divide 7/12 ÷ 3/4

8. Find the reciprocal of 3/10

9. Use an area model to divide 3/4 ÷ 2/3

10. Find the quotient of 1/2 ÷ 4/5

### What have we learned:

• Understand how to divide a fraction by another fraction.

• Understand the rules of the fractions division.

• Write the reciprocal of the divisor.

• Use area models to divide fractions.

• Use number line to find the fractions division.

• Use fraction bars to find the quotient.

• Solve problems on fractions division using models.

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