Divide Fractions – Concept and Examples

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.