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Multiplying Algebraic Fractions

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

'Multiplying Algebraic Fractions' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Use and Interpret Algebraic Notation

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

When we multiply algebraic fractions, we try to reduce or cancel down any top term with a bottom term that has a common factor.

 

Example

Simplify:

a3 x 5
10 7a2

 

Answer

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 x 5
10 7a2

 

= 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:

a2 x 5
10 7a

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

1.

2.

3.

Simplify the following and select the correct answer:

a x 5
10 7a2

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 5
10 7

 


  Answers

1. 2a   2. 20a   3. 1
7 7 70a

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 4
6a 7

 


  Answers

1. 16a   2. 8   3. 8a
42 21 21

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 4a
9 7a

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 4a
9 7

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 6a
9 7

 


  Answers

1. 8a2   2. 24a   3. 16a2
21 63 63

 

1.

2.

3.

Simplify the following and select the correct answer:

4a x 6a
9a 8

 


  Answers

1. 24a2   2. a   3. a2
72 3 3

 

1.

2.

3.

Simplify the following and select the correct answer:

3a x 6a
9a 15a

 


  Answers

1. 6a2   2. 2a   3. 2
135 15 15

 

1.

2.

3.

Simplify the following and select the correct answer:

3a2 x 5a
9 15a

 


  Answers

1. a2   2. 15a2   3. 3a
9 9 15

 

1.

2.

3.

  • Question 1

Simplify the following and select the correct answer:

a2 x 5
10 7a

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

CORRECT ANSWER
1.
  • Question 2

Simplify the following and select the correct answer:

a x 5
10 7a2

 


  Answers

1. a   2. 5a   3. 1
14 10 14a

 

CORRECT ANSWER
3.
  • Question 3

Simplify the following and select the correct answer:

4a x 5
10 7

 


  Answers

1. 2a   2. 20a   3. 1
7 7 70a

 

CORRECT ANSWER
1.
  • Question 4

Simplify the following and select the correct answer:

4a x 4
6a 7

 


  Answers

1. 16a   2. 8   3. 8a
42 21 21

 

CORRECT ANSWER
2.
  • Question 5

Simplify the following and select the correct answer:

4a x 4a
9 7a

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

CORRECT ANSWER
2.
  • Question 6

Simplify the following and select the correct answer:

4a x 4a
9 7

 


  Answers

1. 16a   2. 16a   3. 16a2
7 63 63

 

CORRECT ANSWER
3.
  • Question 7

Simplify the following and select the correct answer:

4a x 6a
9 7

 


  Answers

1. 8a2   2. 24a   3. 16a2
21 63 63

 

CORRECT ANSWER
1.
  • Question 8

Simplify the following and select the correct answer:

4a x 6a
9a 8

 


  Answers

1. 24a2   2. a   3. a2
72 3 3

 

CORRECT ANSWER
2.
  • Question 9

Simplify the following and select the correct answer:

3a x 6a
9a 15a

 


  Answers

1. 6a2   2. 2a   3. 2
135 15 15

 

CORRECT ANSWER
3.
  • Question 10

Simplify the following and select the correct answer:

3a2 x 5a
9 15a

 


  Answers

1. a2   2. 15a2   3. 3a
9 9 15

 

CORRECT ANSWER
1.
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