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Dividing Algebraic Fractions

In this worksheet, students divide algebraic fractions giving their answers as a single fraction.

'Dividing Algebraic Fractions' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use and Interpret Algebraic Notation

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

When we divide algebraic fractions, we use the same method as when we divide numerical fractions. 

First we invert the second fraction and then turn the ÷ sign into a x sign.

Then we try to reduce or cancel down any top term with a bottom term that has a common factor.

 

Example

Simplify:

a3 ÷ 7a2
10 5

 

Answer

a3 ÷ 7a2
10 5

 

Invert the second fraction and change the ÷ sign to a x sign.

 

a3 x 5
10 7a2

 

We look for any top term which has a common factor with any bottom term.

If we find such a reduceable pair of terms, we divide them by their common factor.

 

= a3 ÷ a2 x 5
10
 7a2 ÷ a2

  

= a
x 5
10
 7

  

= a
x 5 ÷ 5
10 ÷ 5
 7

 

= a x 1
2  7

 

= a
14

 

Simplify the following and select the correct answer:

4a ÷ 8
10 5

 


  Answers

1. 16a   2. a   3. 1
5 4 50a

 

1.

2.

3.

Simplify the following and select the correct answer:

a2 ÷ 7a
10 5

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

1.

2.

3.

Simplify the following and select the correct answer:

a ÷ 5a2
10 4

 


  Answers

1. 2a   2. 5a   3. 2
25 2 25a

 

1.

2.

3.

Simplify the following and select the correct answer:

4a ÷ 4
6a 9

 


  Answers

1. 3a   2. 3   3. 8a
2 2 27

 

1.

2.

3.

Simplify the following and select the correct answer:

4a ÷ 7a
9 4a

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

1.

2.

3.

Simplify the following and select the correct answer:

4a ÷ 10
9 4a

 


  Answers

1. 8a2   2. 8a   3. 10
45 45 9

 

1.

2.

3.

Simplify the following and select the correct answer:

4a ÷ 6a
9 18

 


  Answers

1. 4a2   2. 4a   3. 4
3 3 3

 

1.

2.

3.

Simplify the following and select the correct answer:

4a ÷ 4
9a 3a

 


  Answers

1. 24a2   2. a   3. a2
72 3 3

 

1.

2.

3.

Simplify the following and select the correct answer:

3a ÷ 10a
9a 4a

 


  Answers

1. 6a2   2. 2a   3. 2
135 15 15

 

1.

2.

3.

Simplify the following and select the correct answer:

3a2 ÷ 5a2
9 3a

 


  Answers

1. a2   2. 15a3   3. a
5 27 5

 

1.

2.

3.

  • Question 1

Simplify the following and select the correct answer:

4a ÷ 8
10 5

 


  Answers

1. 16a   2. a   3. 1
5 4 50a

 

CORRECT ANSWER
2.
  • Question 2

Simplify the following and select the correct answer:

a2 ÷ 7a
10 5

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

CORRECT ANSWER
1.
  • Question 3

Simplify the following and select the correct answer:

a ÷ 5a2
10 4

 


  Answers

1. 2a   2. 5a   3. 2
25 2 25a

 

CORRECT ANSWER
3.
  • Question 4

Simplify the following and select the correct answer:

4a ÷ 4
6a 9

 


  Answers

1. 3a   2. 3   3. 8a
2 2 27

 

CORRECT ANSWER
2.
  • Question 5

Simplify the following and select the correct answer:

4a ÷ 7a
9 4a

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

CORRECT ANSWER
2.
  • Question 6

Simplify the following and select the correct answer:

4a ÷ 10
9 4a

 


  Answers

1. 8a2   2. 8a   3. 10
45 45 9

 

CORRECT ANSWER
1.
  • Question 7

Simplify the following and select the correct answer:

4a ÷ 6a
9 18

 


  Answers

1. 4a2   2. 4a   3. 4
3 3 3

 

CORRECT ANSWER
3.
  • Question 8

Simplify the following and select the correct answer:

4a ÷ 4
9a 3a

 


  Answers

1. 24a2   2. a   3. a2
72 3 3

 

CORRECT ANSWER
2.
  • Question 9

Simplify the following and select the correct answer:

3a ÷ 10a
9a 4a

 


  Answers

1. 6a2   2. 2a   3. 2
135 15 15

 

CORRECT ANSWER
3.
  • Question 10

Simplify the following and select the correct answer:

3a2 ÷ 5a2
9 3a

 


  Answers

1. a2   2. 15a3   3. a
5 27 5

 

CORRECT ANSWER
3.
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