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Adding and Subtracting Algebraic Fractions (3)

In this worksheet, students add or subtract algebraic fractions giving their answer as a single fraction.

'Adding and Subtracting Algebraic Fractions (3)' 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 add or subtract two fractions, they must have the same denominator.

We use equivalent fractions to change them into two fractions with the same lowest common denominator.

 

Example

Simplify

a + 5c
3b 6d

 

Answer

We must first find a common multiple of 3b and 6d, which is 6bd.

Then we change each fraction into "6bd" ths.

We multiply top and bottom of the first fraction by 2d.

We multiply top and bottom of the second fraction by b.

 

a + 5c
3b 6d

 

= a x 2d + 5c x b
3b x 2d  6d x b

 

= 2ad + 5bc
6bd 6bd

 

= 2ad + 5bc
6bd

 

Simplify the following and select the correct answer:

2a + 3b
c d

 


Answers

1. 2ad +3bc   2. 2ad + 3bc   3. ac + db
c cd bc

 

1.

2.

3.

Simplify the following and select the correct answer:

a + 3d
4b c

 

 

Answers

1. 2ac + 3bd   2. ac + 12bd   3. ac + db
c 4bc 4bc

 

 

1.

2.

3.

Simplify the following and select the correct answer:

5c - b
a d

 


Answers

1. 5cd - db   2. 5cd - ab   3. 5c - b
ac ad ad

 

1.

2.

3.

Simplify the following and select the correct answer:

a - b
2n 4m

 


Answers

1. 2am - bn   2. 2ab - nm   3. a - b
4nm 2 4nm

 

1.

2.

3.

Simplify the following and select the correct answer:

a + b
5p 3q

 


Answers

1. 3aq + 5pb   2. 3qa + pb   3. a + b
15pq 15qp 15pq

 

1.

2.

3.

Simplify the following and select the correct answer:

m + m
n 2n

 


Answers

1. 3m   2. 2m   3. 2m
2n 2n 3n

 

1.

2.

3.

Simplify the following and select the correct answer:

3a + a
b 3b

 


Answers

1. 4a   2. 10a   3. 4a
3b 3b 3b2

 

1.

2.

3.

Simplify the following and select the correct answer:

3a - 1
b 3b

 


Answers

1. 9a - 1   2. 9a - b   3. 9a - b
3b 3b -2b

 

1.

2.

3.

Simplify the following and select the correct answer:

3a - b
7c 5c

 


Answers

1. 15a - 2b   2. 15ac - 7bc   3. 15a - 7b
2c 35c 35c

 

1.

2.

3.

Simplify the following and select the correct answer:

3a - 2b
10b 5d

 


Answers

1. 15ad - 2b   2. 15ad - 2b   3. 3ad - 4b2
10bd 50bd 10bd

 

1.

2.

3.

  • Question 1

Simplify the following and select the correct answer:

2a + 3b
c d

 


Answers

1. 2ad +3bc   2. 2ad + 3bc   3. ac + db
c cd bc

 

CORRECT ANSWER
2.
  • Question 2

Simplify the following and select the correct answer:

a + 3d
4b c

 

 

Answers

1. 2ac + 3bd   2. ac + 12bd   3. ac + db
c 4bc 4bc

 

 

CORRECT ANSWER
2.
  • Question 3

Simplify the following and select the correct answer:

5c - b
a d

 


Answers

1. 5cd - db   2. 5cd - ab   3. 5c - b
ac ad ad

 

CORRECT ANSWER
2.
  • Question 4

Simplify the following and select the correct answer:

a - b
2n 4m

 


Answers

1. 2am - bn   2. 2ab - nm   3. a - b
4nm 2 4nm

 

CORRECT ANSWER
1.
  • Question 5

Simplify the following and select the correct answer:

a + b
5p 3q

 


Answers

1. 3aq + 5pb   2. 3qa + pb   3. a + b
15pq 15qp 15pq

 

CORRECT ANSWER
1.
  • Question 6

Simplify the following and select the correct answer:

m + m
n 2n

 


Answers

1. 3m   2. 2m   3. 2m
2n 2n 3n

 

CORRECT ANSWER
1.
  • Question 7

Simplify the following and select the correct answer:

3a + a
b 3b

 


Answers

1. 4a   2. 10a   3. 4a
3b 3b 3b2

 

CORRECT ANSWER
2.
  • Question 8

Simplify the following and select the correct answer:

3a - 1
b 3b

 


Answers

1. 9a - 1   2. 9a - b   3. 9a - b
3b 3b -2b

 

CORRECT ANSWER
1.
  • Question 9

Simplify the following and select the correct answer:

3a - b
7c 5c

 


Answers

1. 15a - 2b   2. 15ac - 7bc   3. 15a - 7b
2c 35c 35c

 

CORRECT ANSWER
3.
  • Question 10

Simplify the following and select the correct answer:

3a - 2b
10b 5d

 


Answers

1. 15ad - 2b   2. 15ad - 2b   3. 3ad - 4b2
10bd 50bd 10bd

 

CORRECT ANSWER
3.
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