 # Solve Simple Equations with Fractions

In this worksheet, students will learn how to solve linear equations which contain fractions. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra

Curriculum subtopic:   Solving Equations and Inequalities, Algebraic Equations

Difficulty level:   ### QUESTION 1 of 10

"I think of a number, divide by 5, then add 4 and the answer is 7. What number am I thinking of?"

If you have completed any of the previous 'Equations' activities you will be familiar with this sort of puzzle. So what is different about this one? Well, this is the first puzzle to include division and this is important when we think about how to write it as an equation. When writing algebra we do not use the '÷' symbol but we write it as a fraction. So in order to write this puzzle as an equation with x as the unknown number we write: Other than this there is no difference between this and other 2-step equations. In this case, x has been divided by 5 the had 4 added. To solve it we must apply the inverse operations in the reverse order. So first we subtract 4 then we multiply by 5, remembering to do the same to both sides.

We set out our working as follows: So the number I thought of was 15.

Here is another equation, slightly different. Notice here that the line goes under the 'x - 12', not just the 'x'. This changes the order, meaning that starting with x, first, we subtract 12 then divide by 3. So applying inverses in reverse order we must multiply by 3 then add 12.  Here is our working. Get the hang of it?

Note: Sometimes you might see these equations written slightly differently. can also be written as x/5 + 4 = 7. can also be written as (x - 12)/3 = 7.

You should watch out for these, they have been used in some of the questions. Have a go at them now.

Choose the correct solution to the equation x = -1

x = 10

x = 13

x = 17

Here's an equation with a different letter. Which of these is the correct solution?

n = 3

n = 8

n = 33

n = 48

Can you solve this equation? Solve the following equation. Can you match the following equations to their solutions?

## Column B

x/7 = 5
x = 32
x/3 = 8
x = 28
x/4 - 3 = 5
x = 24
x/4 - 5 = 2
x = 35

Can you match each equation to its solution?

## Column B

4y/5 + 6 = 18
y = 12
3y/4 - 1 = 8
y = 5
7y/3 + 5 = 12
y = 15
8y/5 + 3 = 11
y = 3

x = 8 is the solution to which of these equations. There may be more than one correct answer here.

(2x - 1)/3 = 5

(5x + 2)/2 = 23

(4x + 3)/5 = 7

(8x - 9)/5 = 10

Which of these equations has the solution x = -20 (you may choose more than one)?

x/4 = -5

(x - 4)/8 = -4

x/5 + 9 = 5

(3x + 24)/2 = -10

Can you match the equations to their solutions?

Solve the equation • Question 1

Choose the correct solution to the equation x = 10
EDDIE SAYS
Did you get it right? x has been divided by 2 then had 7 added. So to solve we need to subtract 7 then multiply by 2. x/2 + 7 = 12 -7 -7 x/2 = 5 x 2 x 2 x = 10
• Question 2

Here's an equation with a different letter. Which of these is the correct solution?

n = 48
EDDIE SAYS
How did you do? Remember the letter is not important, it just stands for something we don't know The inverse of '÷ 4' is 'x4' and the inverse of '-5' is '+5'. So the solution is: n/4 - 5 = 7 +5 +5 n/4 = 12 x4 x4 n = 48
• Question 3

Can you solve this equation? p = 7
p=7
p =7
p= 7
7
EDDIE SAYS
You ought to be getting the hang of these now. To solve we need to x3 then -17. (p + 17) / 3 = 8 x 3 x3 p + 17 = 24 -17 -17 p = 7
• Question 4

Solve the following equation. EDDIE SAYS
The numbers are a bit bigger here, but the method is just the same. (s - 38) / 11 = 12 x11 x11 s - 38 = 132 +38 +38 s = 170
• Question 5

Can you match the following equations to their solutions?

## Column B

x/7 = 5
x = 35
x/3 = 8
x = 24
x/4 - 3 = 5
x = 32
x/4 - 5 = 2
x = 28
EDDIE SAYS
There is a lot to work through here and take up a lot of space so we'll keep it brief. Here are the inverses in the correct order for each equation. x/7 = 5 → x7 → x = 35 x/3 = 8 → x3 → x = 24 x/4 - 3 = 5 → +3 then x4 → x = 32 x/4 - 5 = 2 → +5 then x4 → x = 28 Did you get them all right? If so, 'well done!'
• Question 6

Can you match each equation to its solution?

## Column B

4y/5 + 6 = 18
y = 15
3y/4 - 1 = 8
y = 12
7y/3 + 5 = 12
y = 3
8y/5 + 3 = 11
y = 5
EDDIE SAYS
Did you spot that these are actually 3-step equations? Again, here are shortened solutions. 4y/5 + 6 = 18 → -6 then x5 then ÷4 → y = 15 3y/4 - 1 = 8 → +1 then x4 then ÷3 → y = 12 7y/3 + 5 = 12 → -5 then x3 then ÷7 → y = 3 8y/5 + 3 = 11 → -3 then x5 then ÷8 → y = 5 How are you doing? Don't worry if you make mistakes, as long as you can see why you went wrong.
• Question 7

x = 8 is the solution to which of these equations. There may be more than one correct answer here.

(2x - 1)/3 = 5
(4x + 3)/5 = 7
EDDIE SAYS
These have 3 steps to them as well. We can check each equation by replacing the x with 8 and seeing if it gives the right answer. (2x - 1)/3 = 5 → (2 x 8 - 1)/3 = 15 ÷3 = 5 (correct) (5x + 2)/2 = 23 → (5 x 8 + 2)/2 = 42 ÷2 = 21 (wrong) (4x + 3)/5 = 7 → (4 x 8 + 3)/5 = 35 ÷5 = 7 (correct) (8x - 9)/5 = 10 → (8 x 8 - 9)/5 = 55 ÷5 = 11 (wrong) So two of them were correct. Did you get them both?
• Question 8

Which of these equations has the solution x = -20 (you may choose more than one)?

x/4 = -5
x/5 + 9 = 5
EDDIE SAYS
Remember, you can check each equation by replacing x with -20 x/4 = -5 → -20 ÷4 = -5 (correct) (x - 4)/8 = -4 → (-20 - 4)/8 = -24 ÷8 = -3 (wrong) x/5 + 9 = 5 → -20 ÷5 + 9 = -4 + 9 = 5 (correct) (3x + 24)/2 = -10 → (3 x -20 + 24)/2 = -36 ÷2 = -18 (wrong) So this time there were 2 correct answers again. How did you do?
• Question 9

Can you match the equations to their solutions?

EDDIE SAYS
Let's work out each equation to see which solution matches. 2n/3 = 8 → x3 then ÷2 → n = 12 n/2 + 7 = 12 → -7 then x2 → n = 10 (n - 7)/4 = 1 → x4 then +7 → n = 11 (5n + 1)/6 = 11 → x6 then -1 then ÷5 → n = 13 How did you do on these? Just one more left to do now.
• Question 10

Solve the equation EDDIE SAYS
This is a tricky one! There are some nasty numbers here but the method is still the same. 3x/4 + 2 = -5.5 -2 -2 3x/4 = -7.5 x4 x4 3x = -30 ÷3 ÷3 x = -10 If you got this one right you are an equation solving expert! And that's the end of the worksheet. Well done - give yourself a pat on the back.
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started 