National 5MathsSQAApplications of MathematicsRevision NotesNumeracy SkillsFractions & PercentagesPercentage Change

Percentage Change (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Dan Finlay

Written by: Dan Finlay

Reviewed by: Roger B

Updated on

Percentage change

How do I increase an amount by a percentage?

  • STEP 1
    Find the decimal multiplier

    • Add the percentage to 100%

      • e.g. 100% + 20% = 120%

    • Divide by 100 to turn into a decimal

      • e.g. 120 ÷ 100 = 1.2

  • STEP 2
    Multiply the amount by the multiplier

    • e.g. increase £250 by 20%

      • £250 × 1.2 = £300

How do I decrease an amount by a percentage?

  • STEP 1
    Find the decimal multiplier

    • Subtract the percentage from 100%

      • e.g. 100% - 30% = 70%

    • Divide by 100 to turn into a decimal

      • e.g. 70 ÷ 100 = 0.7

  • STEP 2
    Multiply the amount by the multiplier

    • e.g. decrease £420 by 30%

      • £420 × 0.7 = £294

Examiner Tips and Tricks

The multiplier will be bigger than 1 for an increase and less than 1 for a decrease.

Worked Example

Lachlan earned £32,800 last year. This year, he earned 12% more.

Calculate how much Lachlan earned this year.

Answer:

STEP 1

Find the decimal multiplier for a 12% increase

table row cell 100 percent sign plus 12 percent sign end cell equals cell 112 percent sign end cell row cell 112 divided by 100 end cell equals cell 1.12 end cell end table

STEP 2

Multiply last year's earnings by the multiplier

£ 32 comma 800 cross times 1.12 equals £ 36 comma 736

£36,736

Worked Example

It took Maisie 350 minutes to complete a race last year.

This year, she took 6% less time to complete the race.

Calculate how long it took Maisie to complete the race this year.

Answer:

STEP 1

Find the decimal multiplier for a 6% decrease

table row cell 100 percent sign minus 6 percent sign end cell equals cell 94 percent sign end cell row cell 94 divided by 100 end cell equals cell 0.94 end cell end table

STEP 2

Multiply last year's time by the multiplier

350 cross times 0.94 equals 329

329 minutes

How do I find the percentage increase or decrease?

  • STEP 1
    Calculate the amount that the quantity has increased or decreased by

    • Find the difference between the original quantity and the new quantity

      • e.g. £400 to £340 is a £60 decrease

  • STEP 2
    Write the difference as a fraction over the original quantity

    • e.g. 60 over 400

  • STEP 3
    Convert the fraction to a percentage

    • e.g. 60 over 400 cross times 100 equals 15

      • £400 to £340 is a 15% decrease

Worked Example

At the start of the summer, Fiona's sunflower was 8.40 cm tall.

At the end of the summer, the sunflower was 11.34 cm tall.

Find the percentage increase of the height of the sunflower from the start of the summer to the end.

Answer:

STEP 1

Calculate the actual increase in the height

11.34 minus 8.40 equals 2.94

STEP 2

Write the actual increase as a fraction over the original height

fraction numerator 2.94 over denominator 8.40 end fraction

STEP 3

Convert the fraction to a percentage

fraction numerator 2.94 over denominator 8.40 end fraction cross times 100 equals 35

35% increase

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Author
Reviewer
Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Roger B

Reviewer: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.