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Algebra: Equations with Fractions (2)

In this worksheet, students solve equations with fractions.

'Algebra: Equations with Fractions (2)' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

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

Difficulty level:  

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:

 

a + a = 14
2 5

 

Answer

 

a + a = 14
2 5

 

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

Each part must be multiplied.

 

10 x a + 10 x a = 10 x 14
2 5

 

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

  

5 10 x a + 2 10 x a = 10 x 14
2 5

  

Simplify

5a + 2a = 140

 

Simplify again

7a = 140

Divide both sides by 7

7a ÷ 7 = 140 ÷ 7

 

Simplify

a = 20

Solve the following equation for a:

 

a + a = 7
2 5

  

(just write the value of a)

Solve the following equation for a:

 

a + a = 15
2 3

  

(just write the value of a)

Solve the following equation for a:

 

a - a = 20
2 3

  

(just write the value of a)

Solve the following equation for a:

 

a + a = 21
2 5

  

(just write the value of a)

Solve the following equation for a:

 

a + a = 12
2 4

  

(just write the value of a)

Solve the following equation for a:

 

a - a = 12
2 5

  

(just write the value of a)

Solve the following equation for a:

 

a - a = 25
2 7

  

(just write the value of a)

Solve the following equation for a:

 

a + a = 24
3 5

  

(just write the value of a)

Solve the following equation for a:

 

a + a = 45
4 5

  

(just write the value of a)

Solve the following equation for a:

 

a - a = 14
3 12

  

(just write the value of a)

  • Question 1

Solve the following equation for a:

 

a + a = 7
2 5

  

(just write the value of a)

CORRECT ANSWER
10
EDDIE SAYS

Multiply both sides by the denominator 10.

Then simply

5a + 2a = 70

  • Question 2

Solve the following equation for a:

 

a + a = 15
2 3

  

(just write the value of a)

CORRECT ANSWER
18
EDDIE SAYS

Multiply both sides by the denominator 6.

Then simply

3a + 2a = 90

  • Question 3

Solve the following equation for a:

 

a - a = 20
2 3

  

(just write the value of a)

CORRECT ANSWER
120
EDDIE SAYS

Multiply both sides by the denominator 6.

Then simply

3a - 2a = 120

  • Question 4

Solve the following equation for a:

 

a + a = 21
2 5

  

(just write the value of a)

CORRECT ANSWER
30
EDDIE SAYS

Multiply both sides by the denominator 10.

Then simply

5a + 2a = 210

  • Question 5

Solve the following equation for a:

 

a + a = 12
2 4

  

(just write the value of a)

CORRECT ANSWER
16
EDDIE SAYS

Multiply both sides by the denominator 4.

Then simply

2a + a = 48

  • Question 6

Solve the following equation for a:

 

a - a = 12
2 5

  

(just write the value of a)

CORRECT ANSWER
40
EDDIE SAYS

Multiply both sides by the denominator 10.

Then simply

5a - 2a = 120

  • Question 7

Solve the following equation for a:

 

a - a = 25
2 7

  

(just write the value of a)

CORRECT ANSWER
70
EDDIE SAYS

Multiply both sides by the denominator 14.

Then simply

7a - 2a = 350

  • Question 8

Solve the following equation for a:

 

a + a = 24
3 5

  

(just write the value of a)

CORRECT ANSWER
45
EDDIE SAYS

Multiply both sides by the denominator 15.

Then simply

8a + 3a = 360

  • Question 9

Solve the following equation for a:

 

a + a = 45
4 5

  

(just write the value of a)

CORRECT ANSWER
100
EDDIE SAYS

Multiply both sides by the denominator 20.

Then simply

5a + 4a = 900

  • Question 10

Solve the following equation for a:

 

a - a = 14
3 12

  

(just write the value of a)

CORRECT ANSWER
56
EDDIE SAYS

Multiply both sides by the denominator 12.

Then simplify

4a - a = 168

---- OR ----

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