# Algebra: Equations with Fractions (1)

In this worksheet, students solve equations with fractions.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:

### QUESTION 1 of 10

There are several ways to solve equations with fractions.

The easiest way is to multiply the whole equation by the denominator (bottom part) of the fraction.  This will eliminate the fraction and the equation can then be solved normally.

Example

Solve the following equation for a:

 5a + 3 = 19 2

 5a + 3 = 19 2

Multiply both sides by the denominator 2.

 2 × 5a + 3 = 2 × 19 2

The 2s cancel out on the left hand side and we get 2 x 19 on the right hand side.

 2 × 5a + 3 = 2 × 19 2

Simplify

5a + 3 = 38

Subtract 3 from both sides.

5a + 3 - 3 = 38  - 3

Simplify

5a = 35

Divide both sides by 5

5a ÷ 5 = 35 ÷ 5

Simplify

a = 7

Solve the following equation for a:

 2a + 4 = 6 3

(just write the value of a)

Solve the following equation for a:

 3a + 4 = 5 5

(just write the value of a)

Solve the following equation for a:

 3a - 1 = 2 7

(just write the value of a)

Solve the following equation for a:

 3a - 4 = 4 5

(just write the value of a)

Solve the following equation for a:

 7a + 3 = 8 3

(just write the value of a)

Solve the following equation for a:

 2a + 10 = 2 3

(just write the value of a)

Solve the following equation for a:

 4a + 32 = 6 3

(just write the value of a)

Solve the following equation for a:

 4a - 2 = 2 4

(just write the value of a)

Solve the following equation for a:

 5a - 11 = 11 4

(just write the value of a)

Solve the following equation for a:

 2a - 11 = 2 4

(just write the value of a)

• Question 1

Solve the following equation for a:

 2a + 4 = 6 3

(just write the value of a)

7
EDDIE SAYS

Multiply both sides by the denominator 3.

Then simply

2a + 4 = 18

• Question 2

Solve the following equation for a:

 3a + 4 = 5 5

(just write the value of a)

7
EDDIE SAYS

Multiply both sides by the denominator 5.

Then simply

3a + 4 = 25

• Question 3

Solve the following equation for a:

 3a - 1 = 2 7

(just write the value of a)

5
EDDIE SAYS

Multiply both sides by the denominator 7.

Then simply

3a - 1 = 14

• Question 4

Solve the following equation for a:

 3a - 4 = 4 5

(just write the value of a)

8
EDDIE SAYS

Multiply both sides by the denominator 5.

Then simply

3a - 4 = 20

• Question 5

Solve the following equation for a:

 7a + 3 = 8 3

(just write the value of a)

3
EDDIE SAYS

Multiply both sides by the denominator 3.

Then simply

7a + 3 = 24

• Question 6

Solve the following equation for a:

 2a + 10 = 2 3

(just write the value of a)

-2
EDDIE SAYS

Multiply both sides by the denominator 3.

Then simply

2a + 10 = 6

2a = -4

a = -2

• Question 7

Solve the following equation for a:

 4a + 32 = 6 3

(just write the value of a)

-3.5
EDDIE SAYS

Multiply both sides by the denominator 3.

Then simply

4a + 32 = 18

4a = -14

a = -3.5

• Question 8

Solve the following equation for a:

 4a - 2 = 2 4

(just write the value of a)

2.5
EDDIE SAYS

Multiply both sides by the denominator 4.

Then simply

4a - 2 = 8

• Question 9

Solve the following equation for a:

 5a - 11 = 11 4

(just write the value of a)

11
EDDIE SAYS

Multiply both sides by the denominator 4.

Then simply

5a - 11 = 44

• Question 10

Solve the following equation for a:

 2a - 11 = 2 4

(just write the value of a)

9.5
EDDIE SAYS

Multiply both sides by the denominator 4.

Then simply

2a - 11 = 8

---- OR ----

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