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Understand Equations with Fractions

In this worksheet, students will learn how to solve equations with fractions.

'Understand Equations with Fractions' worksheet

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Solve Linear Equations (One Variable)

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 (LCM) of the denominator (bottom part) of the fraction. This will eliminate the fractions and the equation can then be solved normally.

 

Example:

Solve the equation below.

 

11a - 2 = 12a + 1
6 7

 

Answer:

 

11a - 2 = 12a + 1
6 7

 

 

Multiply both sides by the LCM of 6 and 7 which is 42.

Then, put brackets around the numerators (top parts).

 

42 × (11a - 2) = 42 × (12a + 1)
  6   7

 

Reduce the fractions:

 

7 42 × (11a - 2) = 6 42 × (12a + 1)
  6   7

 

Simplify:

7 (11a - 2) = 6 (12a + 1)

 

Multiply out the brackets:

77a - 14 = 72a + 6

 

Add 14 to both sides:

77a - 14 + 14 = 72a + 6 + 14

 

Simplify:

77a = 72a + 20

 

Subtract 72a from both sides:

77a -72a = 72a + 20 - 72a

 

Simplify:

5a = 20

 

Divide both sides by 5:

5a ÷ 5 = 20 ÷ 5

 

Simplify:

a = 4

 

Ensure you have a pen and paper so that you can write down your working out. This will enable you to spot any errors and, even if you get the final answer incorrect in your exams you main still gain valuable marks.

 

Solve the equation below.

  

a + 2 = a + 4
5 7

 

 

What is the value of a?

Solve the equation below.

  

a + 2 = a + 12
4 9

 

 

What is the value of a?

6

12

4

2

Solve the equation below.

  

a + 1 = a + 6
7 12

 

 

What is the value of a?

Solve the following equation for a.

  

a - 1 = a + 4
3 8

 

 

What is the value of a?

Solve the following equation to find a.

 

  

a - 4 = a - 1
8 11

Solve the following equation for a.

  

a - 4 = a - 11
3 10

 

 

1

15

12

4

Solve the following equation for a.

  

3a + 2 = 6a + 11
2 5

 

 

 

1

15

12

4

Solve the following equation for a.

  

4a + 3 = 6a + 7
3 5

 

 

What is the value of a?

Solve the following equation to find a.

  

7a + 3 = 5a - 1
12 7

 

 

 

Solve the following equation for a.

 

  

7a - 10 = 8a - 5
5 7

 

 

 

  • Question 1

Solve the equation below.

  

a + 2 = a + 4
5 7

 

 

What is the value of a?

CORRECT ANSWER
3
EDDIE SAYS
First, you need to identify the LCM of 5 and 7 = 35. Then you put brackets around the numerators 35 (a + 2) = 35 (a + 4) and reduce the fractions: 7 (a + 2) = 5 (a + 4) Multiply out the brackets: 7a + 14 = 5a + 20 Minus 14 from both sides: 7a = 5a + 6 Minus 5a from both sides: 2a = 6 Simplify: a = 3 Phew, that was a challenge! How did you get on?
  • Question 2

Solve the equation below.

  

a + 2 = a + 12
4 9

 

 

What is the value of a?

CORRECT ANSWER
6
EDDIE SAYS
The LCM of 9 and 4 = 36. Then you put brackets around the numerators 36 (a + 2) = 36 (a + 12) and reduce the fractions: 9 (a + 2) = 4 (a + 12) Multiply out the brackets: 9a + 18 = 4a + 48 Minus 4a from both sides: 5a + 18 = 48 Minus 18 from both sides: 5a = 30 Simplify: a = 6
  • Question 3

Solve the equation below.

  

a + 1 = a + 6
7 12

 

 

What is the value of a?

CORRECT ANSWER
6
EDDIE SAYS
The LCM of 7 and 12 = 84. Then you put brackets around the numerators 84 (a + 1) = 84 (a + 6) and reduce the fractions: 12 (a + 1) = 7 (a + 6) Multiply out the brackets: 12a + 12 = 7a + 42 Minus 7a from both sides: 5a + 12 = 42 Minus 12 from both sides: 5a = 30 Simplify: a = 6 Great focus! Hopefully, you're beginning to get your head around these.
  • Question 4

Solve the following equation for a.

  

a - 1 = a + 4
3 8

 

 

What is the value of a?

CORRECT ANSWER
4
EDDIE SAYS
The LCM of 3 and 8 = 24. Then you put brackets around the numerators 24 (a - 1) = 24 (a + 4) and reduce the fractions: 8 (a - 1) = 3 (a + 4) Multiply out the brackets: 8a - 8 = 3a + 12 Minus 3a from both sides: 5a - 8 = 12 Add 8 to both sides: 5a = 20 Simplify: a = 4 Take a deep breath, you've got this.
  • Question 5

Solve the following equation to find a.

 

  

a - 4 = a - 1
8 11
CORRECT ANSWER
EDDIE SAYS
The LCM of 8 and 11 = 88. Then you put brackets around the numerators 88 (a - 4) = 88 (a - 1) and reduce the fractions: 11 (a - 4) = 8 (a - 1) Multiply out the brackets: 11a - 44 = 8a - 8 Minus 8a from both sides: 3a - 44 = -8 Add 44 to both sides: 3a = 36 Simplify: a = 12
  • Question 6

Solve the following equation for a.

  

a - 4 = a - 11
3 10

 

 

CORRECT ANSWER
1
EDDIE SAYS
The LCM of 3 and 10 = 30 Then you put brackets around the numerators 30 (a - 4) = 30 (a - 11) and reduce the fractions: 10 (a - 4) = 3 (a - 11) Multiply out the brackets: 10a - 40 = 3a - 33 Add 33 to both sides: 10 - 7 = 3a Simplify: 3 = 3a Simplify: a = 1 Is this becoming less daunting? Four more questions to go...
  • Question 7

Solve the following equation for a.

  

3a + 2 = 6a + 11
2 5

 

 

 

CORRECT ANSWER
EDDIE SAYS
The LCM of 2 and 5 = 10. Then you put brackets around the numerators 10 (3a + 2) = 10 (6a + 11) and reduce the fractions: 5 (3a + 2) = 2 (6a + 11) Multiply out the brackets: 15a + 10 = 12a + 22 Minus 10 from both sides: 15a = 12a + 12 Minus 12a from both sides: 3a = 12 Simplify: a = 4 Great work if you got this one right!
  • Question 8

Solve the following equation for a.

  

4a + 3 = 6a + 7
3 5

 

 

What is the value of a?

CORRECT ANSWER
3
EDDIE SAYS
The LCM of 3 and 5 = 15. Then you put brackets around the numerators 15 (4a + 3) = 15 (6a + 7) and reduce the fractions: 5 (4a + 3) = 3 (6a + 7) Multiply out the brackets: 20a + 15 = 18a + 21 Minus 15 from both sides: 20a = 18a + 6 Minus 18a from both sides: 2a = 6 Simplify: a = 3
  • Question 9

Solve the following equation to find a.

  

7a + 3 = 5a - 1
12 7

 

 

 

CORRECT ANSWER
3
EDDIE SAYS
The LCM of 7 and 12 = 84. Then you put brackets around the numerators 84 (7a + 3) = 84 (5a - 1) and reduce the fractions: 7 (7a + 3) = 12 (5a - 1) Multiply out the brackets: 49a + 21 = 60a - 12 Add 12 to both sides: 49a + 33 = 60a Minus 49a from both sides: 33 = 11a Simplify: a = 3 Was this easier or more difficult?
  • Question 10

Solve the following equation for a.

 

  

7a - 10 = 8a - 5
5 7

 

 

 

CORRECT ANSWER
EDDIE SAYS
The LCM of 7 and 5 = 35. Then you put brackets around the numerators 35 (7a - 10) = 35 (8a -5) and reduce the fractions: 7 (7a - 10) = 5 (8a - 5) Multiply out the brackets: 49a - 70 = 40a - 25 Add 25 to both sides: 49a - 45 = 40a Minus 40a from both sides: 9a - 45 = 0 Add 45 to both sides: 9a = 45 Simplify: a = 5 Well done that's another activity ticked off! Take a well-deserved break.
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