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Algebra: Equations with Fractions (3)

In this worksheet, students solve equations with fractions.

'Algebra: Equations with Fractions (3)' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

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

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

There are several ways to solve equations with fractions. 

The easiest way is to multiply the whole equation by the lowest common multiple of the denominators (bottom parts) of the fractions.  This will eliminate the fractions and the equation can then be solved normally.

 

Example

Solve the following equation for a:

 

3a + 2a = 38
2 5

 

Answer

 

3a + 2a = 38
2 5

 

Multiply both sides by 10, which is the l.c.m. of 2 and 5. 

Each part must be multiplied.

 

10 x 3a + 10 x 2a = 10 x 38
2 5

 

Reduce each part of the left hand side and we get 10 x 14 on the right hand side.

  

5 10 x 3a + 2 10 x 2a = 10 x 38
2 5

  

Simplify

5 x 3a + 2 x 2a = 380

 

Simplify again

15a + 4a = 380

Simplify again

19a = 380

 
Divide both sides by 19

19a ÷ 19 = 380 ÷ 19

Simplify

a = 20

Solve the following equation for a:

 

3a + 2a = 19
2 5

  

(just write the value of a)

Solve the following equation for a:

 

a + 2a = 14
2 3

  

(just write the value of a)

Solve the following equation for a:

 

5a - 2a = 22
2 3

  

(just write the value of a)

Solve the following equation for a:

 

a + 4a = 39
2 5

  

(just write the value of a)

Solve the following equation for a:

 

3a + a = 28
2 4

  

(just write the value of a)

Solve the following equation for a:

 

7a - 2a = 124
2 5

  

(just write the value of a)

Solve the following equation for a:

 

7a - 2a = 135
2 7

  

(just write the value of a)

Solve the following equation for a:

 

2a + 3a = 57
3 5

  

(just write the value of a)

Solve the following equation for a:

 

3a + 4a = 124
4 5

  

(just write the value of a)

Solve the following equation for a:

 

2a - 5a = 14
3 12

  

(just write the value of a)

  • Question 1

Solve the following equation for a:

 

3a + 2a = 19
2 5

  

(just write the value of a)

CORRECT ANSWER
10
  • Question 2

Solve the following equation for a:

 

a + 2a = 14
2 3

  

(just write the value of a)

CORRECT ANSWER
12
  • Question 3

Solve the following equation for a:

 

5a - 2a = 22
2 3

  

(just write the value of a)

CORRECT ANSWER
12
  • Question 4

Solve the following equation for a:

 

a + 4a = 39
2 5

  

(just write the value of a)

CORRECT ANSWER
30
  • Question 5

Solve the following equation for a:

 

3a + a = 28
2 4

  

(just write the value of a)

CORRECT ANSWER
16
  • Question 6

Solve the following equation for a:

 

7a - 2a = 124
2 5

  

(just write the value of a)

CORRECT ANSWER
40
  • Question 7

Solve the following equation for a:

 

7a - 2a = 135
2 7

  

(just write the value of a)

CORRECT ANSWER
42
  • Question 8

Solve the following equation for a:

 

2a + 3a = 57
3 5

  

(just write the value of a)

CORRECT ANSWER
45
  • Question 9

Solve the following equation for a:

 

3a + 4a = 124
4 5

  

(just write the value of a)

CORRECT ANSWER
80
  • Question 10

Solve the following equation for a:

 

2a - 5a = 14
3 12

  

(just write the value of a)

CORRECT ANSWER
56
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