# Dividing Algebraic Fractions

In this worksheet, students divide algebraic fractions 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

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

 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

 1 16a 2. a 3. 1 5 4 50a

1.

2.

3.

Simplify the following and select the correct answer:

 a2 ÷ 7a 10 5

 1 a 2. 5a 3. 1 14 10 14a

1.

2.

3.

Simplify the following and select the correct answer:

 a ÷ 5a2 10 4

 1 2a 2. 5a 3. 2 25 2 25a

1.

2.

3.

Simplify the following and select the correct answer:

 4a ÷ 4 6a 9

 1 3a 2. 3 3. 8a 2 2 27

1.

2.

3.

Simplify the following and select the correct answer:

 4a ÷ 7a 9 4a

 1 16a 2. 16a 3. 16a2 7 63 63

1.

2.

3.

Simplify the following and select the correct answer:

 4a ÷ 10 9 4a

 1 8a2 2. 8a 3. 10 45 45 9

1.

2.

3.

Simplify the following and select the correct answer:

 4a ÷ 6a 9 18

 1 4a2 2. 4a 3. 4 3 3 3

1.

2.

3.

Simplify the following and select the correct answer:

 4a ÷ 4 9a 3a

 1 24a2 2. a 3. a2 72 3 3

1.

2.

3.

Simplify the following and select the correct answer:

 3a ÷ 10a 9a 4a

 1 6a2 2. 2a 3. 2 135 15 15

1.

2.

3.

Simplify the following and select the correct answer:

 3a2 ÷ 5a2 9 3a

 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

 1 16a 2. a 3. 1 5 4 50a

2.
• Question 2

Simplify the following and select the correct answer:

 a2 ÷ 7a 10 5

 1 a 2. 5a 3. 1 14 10 14a

1.
• Question 3

Simplify the following and select the correct answer:

 a ÷ 5a2 10 4

 1 2a 2. 5a 3. 2 25 2 25a

3.
• Question 4

Simplify the following and select the correct answer:

 4a ÷ 4 6a 9

 1 3a 2. 3 3. 8a 2 2 27

2.
• Question 5

Simplify the following and select the correct answer:

 4a ÷ 7a 9 4a

 1 16a 2. 16a 3. 16a2 7 63 63

2.
• Question 6

Simplify the following and select the correct answer:

 4a ÷ 10 9 4a

 1 8a2 2. 8a 3. 10 45 45 9

1.
• Question 7

Simplify the following and select the correct answer:

 4a ÷ 6a 9 18

 1 4a2 2. 4a 3. 4 3 3 3

3.
• Question 8

Simplify the following and select the correct answer:

 4a ÷ 4 9a 3a

 1 24a2 2. a 3. a2 72 3 3

2.
• Question 9

Simplify the following and select the correct answer:

 3a ÷ 10a 9a 4a

 1 6a2 2. 2a 3. 2 135 15 15

3.
• Question 10

Simplify the following and select the correct answer:

 3a2 ÷ 5a2 9 3a

 1 a2 2. 15a3 3. a 5 27 5

3.
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