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Equations with Fractions (1)

In this worksheet, students solve equations with fractions.

'Equations with Fractions (1)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Translate Simple Situations or Procedures into Algebraic Expressions, Formulae or Equations

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 × 3a + 10 × 2a = 10 × 38
2 5

 

Reduce each part of the left hand side and we get 10 × 38 on the right hand side.

  

5 10 × 3a + 2 10 × 2a = 10 × 38
2 5

  

Simplify

5 × 3a + 2 × 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 = 12
2 4

  

(just write the value of a)

Solve the following equation for a:

 

a + 2a = 18
2 5

  

(just write the value of a)

Solve the following equation for a:

 

5a - 2a = 42
2 5

  

(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 = 23
2 7

  

(just write the value of a)

Solve the following equation for a:

 

a - 5a = 3
2 9

  

(just write the value of a)

Solve the following equation for a:

 

7a - 2a = 146
2 11

  

(just write the value of a)

Solve the following equation for a:

 

2a + 3a = 93
3 11

  

(just write the value of a)

Solve the following equation for a:

 

3a + 4a = 34
10 15

  

(just write the value of a)

Solve the following equation for a:

 

2a - 11a = 14
3 12

  

(just write the value of a)

  • Question 1

Solve the following equation for a:

 

3a + 2a = 12
2 4

  

(just write the value of a)

CORRECT ANSWER
6
EDDIE SAYS

l.c.m. is 4. 

4 x 3a + 4 x 2a = 4 x 12
2 4

Then simplify

2 x 3a + 2a = 48

  • Question 2

Solve the following equation for a:

 

a + 2a = 18
2 5

  

(just write the value of a)

CORRECT ANSWER
20
EDDIE SAYS

l.c.m. is 10. 

10 x a + 10 x 2a = 10 x 18
2 5

Then simplify

5 x a + 2 x 2a = 180

  • Question 3

Solve the following equation for a:

 

5a - 2a = 42
2 5

  

(just write the value of a)

CORRECT ANSWER
20
EDDIE SAYS

l.c.m. is 10. 

10 x 5a - 10 x 2a = 10 x 42
2 5

Then simplify

5 x 5a - 2 x 2a = 420

  • Question 4

Solve the following equation for a:

 

a - 4a = 39
2 5

  

(just write the value of a)

CORRECT ANSWER
-130
EDDIE SAYS

l.c.m. is 10. 

10 x a - 10 x 4a = 10 x 39
2 5

Then simplify

5 x a - 2 x 4a = 390

  • Question 5

Solve the following equation for a:

 

3a + a = 23
2 7

  

(just write the value of a)

CORRECT ANSWER
14
EDDIE SAYS

l.c.m. is 14.

14 x 3a + 14 x a = 14 x 23
2 7

Then simplify

7 x 3a + 2 x a = 322

  • Question 6

Solve the following equation for a:

 

a - 5a = 3
2 9

  

(just write the value of a)

CORRECT ANSWER
-54
EDDIE SAYS

l.c.m. is 18. 

18 x a - 18 x 5a = 18 x 3
2 9

Then simplify

9 x a - 2 x 5a = 54

-a = 54

a = -54

  • Question 7

Solve the following equation for a:

 

7a - 2a = 146
2 11

  

(just write the value of a)

CORRECT ANSWER
44
EDDIE SAYS

l.c.m. is 22. 

22 x 7a - 22 x 2a = 22 x 146
2 11

Then simplify

11 x 7a - 2 x 2a = 3212

73a = 3212

  • Question 8

Solve the following equation for a:

 

2a + 3a = 93
3 11

  

(just write the value of a)

CORRECT ANSWER
99
EDDIE SAYS

l.c.m. is 33. 

33 x 2a + 33 x 3a = 33 x 93
3 11

Then simplify

11 x 2a + 3 x 3a = 3069

31a = 3069

  • Question 9

Solve the following equation for a:

 

3a + 4a = 34
10 15

  

(just write the value of a)

CORRECT ANSWER
60
EDDIE SAYS

l.c.m. is 30. 

30 x 3a + 30 x 4a = 30 x 34
10 15

Then simplify

3 x 3a + 2 x 4a = 1020

17a = 1020

  • Question 10

Solve the following equation for a:

 

2a - 11a = 14
3 12

  

(just write the value of a)

CORRECT ANSWER
-56
EDDIE SAYS

l.c.m. is 12. 

12 x 2a - 12 x 11a = 12 x 14
3 12

Then simplify

4 x 2a - 11a = 168

-3a = 168

---- OR ----

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