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Maths

Equations with fractions - Higher

In addition to solving simple equations, at the higher level you also need to know how to solve equations with fractions.

# Fractions

How do we solve the equation x/2 − 4 = 3?

One way is to multiply everything by 2:

x/2 − 4 = 3

x - 8 = 6

x = 14

Or, alternatively, add 4 and then multiply both sides by 2:

x/2 − 4 = 3

x/2 = 7

x = 14

Question

Solve the equation: 4 − x/3 = 1

Method 1

4 − x/3 = 1

(multiply by 3) 12 − x = 3

(add x) 12 = 3 + x

(minus 3) x = 9

Method 2

4 − x/3 = 1

(add x/3) 4 = 1 + x/3

(minus 1) 3 = x/3

(multiply 3) x = 9

Question

A number is doubled and divided by 5. This has the same answer as 3 more than the number divided by eight. What is the number?

First write out the information as an equation.

• Call the number x.
• A number is doubled and divided by 5 can be written 2x/5
• And 3 more than the number divided by eight can be written (x + 3)/8.
• So we have
• 2x/5 = (x + 3)/8
• 40 ( 2x/5) = 40 ( (x + 3)/8) (Multiply both sides by 40)
• 8 ( 2x ) = 5 (x + 3) (cancelling out)
• 16x = 5x + 15 (multiplying out the brackets)
• 11x = 15
• So
• x = 15/11 = 1 4/11

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