# Division of Algebraic Terms with Powers (3)

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

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use and Interpret Algebraic Notation

Difficulty level:

### QUESTION 1 of 10

This worksheet is about the division of algebraic terms with powers.

Example

Simplify:

 10a2b5 15a3b2

Remember what 10a2b5 and 15a3b2 mean and divide them by subtracting the relevant indices.

We get:

 10 x a x a x b x b x b x b x b 15 x a x a x a x b x b

Cancel down a matching number of a terms from the top of the fraction with a terms from the bottom.  Similarly with b terms.

This leaves us:

 10 x b x b x b 15 x a

which reduces by dividing top and bottom by 5 to

 2b3 3a

Simplify:

 10a3 15ab

 1. a 2. 2a 3. 2a2 5b 3b 3b

1.

2.

3.

Simplify:

 4p 12q

 1. p 2. p 3. 2p 8q 3q 8q

1.

2.

3.

Simplify:

 8a2 12ab

 1. 2a 2. a 3. a 3b 3b 4b

1.

2.

3.

Simplify:

 8ab 15b2

 1. 2a 2. a 3. 8a 5b 3b 15b

1.

2.

3.

Simplify:

 8a2 16ab2

 1. 2a 2. a 3. 8a b 2b2 16b

1.

2.

3.

Simplify:

 4a2b 6ab2

 1. 2a 2. a 3. 2a 3b 2b2 3b2

1.

2.

3.

Simplify:

 21a3b 14ab4

 1. 3a 2. 3a2 3. 2a 2b3 2b3 3b2

1.

2.

3.

Simplify:

 15a3 24ab4

 1. 3a 2. 5a2 3. 5a 5b3 8b4 8b2

1.

2.

3.

Simplify:

 15x4y2 25xy4

 1. 3x 2. 5x2 3. 3x3 5y3 20y4 5y2

1.

2.

3.

Simplify:

 15x4y3 35y4

 1. 3x4 2. 5x4 3. 3x3 7y 7y4 7y2

1.

2.

3.

• Question 1

Simplify:

 10a3 15ab

 1. a 2. 2a 3. 2a2 5b 3b 3b

3.
• Question 2

Simplify:

 4p 12q

 1. p 2. p 3. 2p 8q 3q 8q

2.
• Question 3

Simplify:

 8a2 12ab

 1. 2a 2. a 3. a 3b 3b 4b

1.
• Question 4

Simplify:

 8ab 15b2

 1. 2a 2. a 3. 8a 5b 3b 15b

3.
• Question 5

Simplify:

 8a2 16ab2

 1. 2a 2. a 3. 8a b 2b2 16b

2.
• Question 6

Simplify:

 4a2b 6ab2

 1. 2a 2. a 3. 2a 3b 2b2 3b2

1.
• Question 7

Simplify:

 21a3b 14ab4

 1. 3a 2. 3a2 3. 2a 2b3 2b3 3b2

2.
• Question 8

Simplify:

 15a3 24ab4

 1. 3a 2. 5a2 3. 5a 5b3 8b4 8b2

2.
• Question 9

Simplify:

 15x4y2 25xy4

 1. 3x 2. 5x2 3. 3x3 5y3 20y4 5y2

3.
• Question 10

Simplify:

 15x4y3 35y4

 1. 3x4 2. 5x4 3. 3x3 7y 7y4 7y2

1.
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