Class 5 - Division of Fractions: Complete Learning Guide

Division of fractions is an important Maths skill that helps Class 5 students to solve the problems in a simple way. In this article students will learn how to divide fractions using simple steps and clear examples.

Table of Contents

• What is Dividing of Fractions?
• Division of Fractions Formula
• Easy Steps to Divide Fractions
• Solved Examples on Division of Fractions
• Practice Questions on Division of Fractions for Class 5
• Division of Fractions Worksheet for Class 5

What is Dividing of Fractions?

Dividing of fractions means to split a fraction into equal parts. Dividing Fractions When we divide fractions, we are asking how many parts of one fraction fit into another fraction. Division of fractions is the reciprocal of multiplication of fractions.

Division of Fractions Formula

When dividing two fractions:

  ab÷cd=adbc

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Easy Steps to Divide Fractions

Step 1: Write the Division Problem

Write the two fractions with the division sign between them. Example: 3/4 ÷ 1/2

Step 2: Keep the First Fraction

Keep the first fraction exactly as it is. Do not change anything. Example: 3/4 stays the same

Step 3: Change the Division Sign

Change the division sign (÷) to a multiplication sign (×). Example: 3/4 × (next comes the reciprocal)

Step 4: Flip the Second Fraction

Take the second fraction and flip it. Write the denominator as the numerator and the numerator as the denominator. This is called the reciprocal. Original second fraction: 1/2 becomes Reciprocal: 2/1

Step 5: Multiply the Fractions

Now multiply the first fraction by the reciprocal of the second fraction. Example: 3/4 × 2/1 = (3 × 2)/(4 × 1) = 6/4

Step 6: Simplify the Answer

Reduce the fraction to its simplest form by dividing both numerator and denominator by their greatest common factor. Example: 6/4 = 3/2 or 1 1/2

Solved Examples on Division of Fractions

Example 1: Dividing Two Simple Fractions

Question: Divide 1/2 by 1/4. What is the answer?

Solution:

Problem: 1/2 ÷ 1/4

Step 1: Keep the first fraction: 1/2

Step 2: Change ÷ to ×: 1/2 ×?

Step 3: Flip the second fraction: 1/4 becomes 4/1

Step 4: Multiply: 1/2 × 4/1 = (1 × 4)/(2 × 1) = 4/2

Step 5: Simplify: 4/2 = 2

Answer: 1/2 ÷ 1/4 = 2

Example 2: Dividing Different Fractions

Question: Divide 3/4 by 1/2. Find the quotient.

Solution:

Problem: 3/4 ÷ 1/2

Step 1: Keep first fraction: 3/4

Step 2: Change ÷ to ×: 3/4 × ?

Step 3: Flip second fraction: 1/2 becomes 2/1

Step 4: Multiply: 3/4 × 2/1 = (3 × 2)/(4 × 1) = 6/4

Step 5: Simplify: 6/4 = 3/2 = 1 1/2

Answer: 3/4 ÷ 1/2 = 3/2 or 1 1/2

Example 3: Dividing Fractions with Larger Numbers

Question: What is 5/6 ÷ 2/3?

Solution:

Problem: 5/6 ÷ 2/3

Step 1: Keep first fraction: 5/6

Step 2: Change ÷ to ×: 5/6 × ?

Step 3: Flip second fraction: 2/3 becomes 3/2

Step 4: Multiply: 5/6 × 3/2 = (5 × 3)/(6 × 2) = 15/12

Step 5: Simplify: 15/12 = 5/4 = 1 1/4

Answer: 5/6 ÷ 2/3 = 5/4 or 1 1/4

Example 4: Dividing a Fraction by a Whole Number

Question: Divide 3/4 by 2. What is the result?

Solution:

Problem: 3/4 ÷ 2

Step 1: Change whole number to fraction: 2 = 2/1

Step 2: New problem: 3/4 ÷ 2/1

Step 3: Keep first fraction: 3/4

Step 4: Change ÷ to ×: 3/4 × ?

Step 5: Flip second fraction: 2/1 becomes 1/2

Step 6: Multiply: 3/4 × 1/2 = (3 × 1)/(4 × 2) = 3/8

Answer: 3/4 ÷ 2 = 3/8

Example 5: Dividing a Whole Number by a Fraction

Question: Divide 3 by 1/4. Find the answer.

Solution:

Problem: 3 ÷ 1/4

Step 1: Change whole number to fraction: 3 = 3/1

Step 2: New problem: 3/1 ÷ 1/4

Step 3: Keep first fraction: 3/1

Step 4: Change ÷ to ×: 3/1 × ?

Step 5: Flip second fraction: 1/4 becomes 4/1

Step 6: Multiply: 3/1 × 4/1 = (3 × 4)/(1 × 1) = 12/1 = 12

Answer: 3 ÷ 1/4 = 12

Example 6: Dividing Mixed Numbers

Question: Divide 1 1/2 by 1/2. What is the quotient?

Solution:

Problem: 1 1/2 ÷ 1/2

Step 1: Convert mixed number to improper fraction: 1 1/2 = 3/2

Step 2: New problem: 3/2 ÷ 1/2

Step 3: Keep first fraction: 3/2

Step 4: Change ÷ to ×: 3/2 × ?

Step 5: Flip second fraction: 1/2 becomes 2/1

Step 6: Multiply: 3/2 × 2/1 = (3 × 2)/(2 × 1) = 6/2 = 3

Answer: 1 1/2 ÷ 1/2 = 3

Example 7: Dividing Fractions That Simplify

Question: Divide 2/5 by 4/5. Find the result.

Solution:

Problem: 2/5 ÷ 4/5

Step 1: Keep first fraction: 2/5

Step 2: Change ÷ to ×: 2/5 × ?

Step 3: Flip second fraction: 4/5 becomes 5/4

Step 4: Multiply: 2/5 × 5/4 = (2 × 5)/(5 × 4) = 10/20

Step 5: Simplify: 10/20 = 1/2

Answer: 2/5 ÷ 4/5 = 1/2

Example 8: Dividing Equal Fractions

Question: What is 3/7 ÷ 3/7?

Solution:

Problem: 3/7 ÷ 3/7

Step 1: Keep first fraction: 3/7

Step 2: Change ÷ to ×: 3/7 × ?

Step 3: Flip second fraction: 3/7 becomes 7/3

Step 4: Multiply: 3/7 × 7/3 = (3 × 7)/(7 × 3) = 21/21 = 1

When any number is divided by itself, the answer is always 1.

Answer: 3/7 ÷ 3/7 = 1

Example 9: Real World Application

Question: Sarah has 3/4 of a chocolate bar. She wants to divide it into pieces of 1/8 each. How many pieces will she have?

Solution:

Problem: 3/4 ÷ 1/8

Step 1: Keep first fraction: 3/4

Step 2: Change ÷ to ×: 3/4 × ?

Step 3: Flip second fraction: 1/8 becomes 8/1

Step 4: Multiply: 3/4 × 8/1 = (3 × 8)/(4 × 1) = 24/4 = 6

Answer: Sarah will have 6 pieces of chocolate.

Example 10: Dividing Multiple Fractions

Question: If you have 2/3 ÷ 1/6 ÷ 2, what is the answer?

Solution:

Problem: 2/3 ÷ 1/6 ÷ 2

Step 1: Solve from left to right. First: 2/3 ÷ 1/6

• Keep: 2/3
• Change ÷ to ×
• Flip: 1/6 becomes 6/1
• Multiply: 2/3 × 6/1 = 12/3 = 4

Step 2: Now divide the answer by 2. 4 ÷ 2 = 2

Answer: 2/3 ÷ 1/6 ÷ 2 = 2

Practice Questions on Division of Fractions for Class 5

1: What do we do to the second fraction when dividing fractions?

(A) Keep it the same

(B) Flip it (take its reciprocal)

(C) Make it bigger

(D) Make it smaller

2: What is 1/2 ÷ 1/2?

(A) 1/4

(B) 1

(C) 2

(D) 1/2

3: What is the first step when dividing 3/4 ÷ 1/2?

(A) Flip both fractions

(B) Keep the first fraction the same

(C) Add the fractions

(D) Subtract the fractions

4: What is 2/3 ÷ 2/3?

(A) 1/3

(B) 4/9

(C) 1

(D) 2

5: To divide 1/2 ÷ 1/4, what do we multiply?

(A) 1/2 × 1/4

(B) 1/2 × 4/1

(C) 2/1 × 1/4

(D) 1/4 × 1/2

6: To divide fractions, we multiply by the reciprocal of the second fraction.

(A) True

(B) False

7: The reciprocal of 3/4 is 4/3.

(A) True

(B) False

8: Any number divided by itself equals 1.

(A) True

(B) False

9: Find the reciprocal of 5/6.

10: Divide 3/5 by 1/2. Show your work.

11: What is 1/3 ÷ 2? Simplify your answer.

12: John has 3/4 of a metre of cloth. He wants to cut it into pieces that are 1/8 metre each. How many pieces will he have?

13: Convert 2 1/4 to an improper fraction and then divide by 1/4.

Division of Fractions Worksheet for Class 5

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