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4.7 Calculating Percentages 1

GCSE Maths Foundation · Edexcel · Chapter 4: Fractions and percentages

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: percentages of amounts, percentage increase and decrease, profit and loss. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Find a percentage of an amount without a calculator using 10%, 5% and 1%
  • Find a percentage of an amount with a calculator using a decimal multiplier
  • Increase or decrease an amount by a percentage
  • Solve problems involving VAT, profit and loss

Key words

  • Multiplier: The decimal you multiply by. Finding 17% means × 0.17; increasing by 17% means × 1.17.
  • VAT: Value Added Tax, added to the price of many goods. In the UK the standard rate is 20%.
  • Cost price: What a shop or person pays for an item.
  • Selling price: What the item is sold for.
  • Profit / loss: Selling price − cost price. If this is negative it is a loss.

Percentages of amounts without a calculator

Find 10% by dividing by 10, 1% by dividing by 100, 5% by halving 10%, 50% by halving the amount. Then build up the percentage you need.

Worked example: building up a percentage

35% of £60: 10% = £6, so 30% = £18; 5% = £3; 35% = £18 + £3 = £21
12% of 450: 10% = 45, 1% = 4.5, 2% = 9; 12% = 45 + 9 = 54

Answer: £21 and 54

Percentages of amounts with a calculator

Write the percentage as a decimal (divide by 100) and multiply.

Worked example: decimal multiplier

17% of 340: 0.17 × 340 = 57.8
6.5% of £2400: 0.065 × 2400 = £156

Answer: 57.8 and £156

Key fact: For money, give answers to 2 decimal places: £9.9 should be written £9.90.

Increasing and decreasing by a percentage

Method 1: find the percentage and add it on (or take it off). Method 2: use a multiplier. An increase of 20% means you will have 120% = 1.20 of the amount. A decrease of 15% leaves 85% = 0.85.

Worked example: increase

Method 1: 20% of £45 = £9; £45 + £9 = £54
Method 2: £45 × 1.2 = £54

Answer: £54

Worked example: decrease

Method 1: 10% = 36, 5% = 18, so 15% = 54; 360 − 54 = 306
Method 2: 360 × 0.85 = 306

Answer: 306

VAT, profit and loss

VAT is a percentage increase. Profit and loss compare the selling price with the cost price. "A 25% profit" means the selling price is 125% of the cost price.

Worked example: VAT

A drill costs £85 plus VAT at 20%. Find the total cost.
£85 × 1.2 = £102

Answer: £102

Worked example: profit and loss

A trader buys a lamp for £80 and sells it at a 25% profit. Find the selling price.
25% of £80 = £20, so the selling price is £80 + £20 = £100.
She buys a chair for £150 and has to sell it at a 10% loss: £150 × 0.9 = £135.

Answer: lamp £100, chair £135 (a loss of £15)

Common mistakes

  • Finding 5% by dividing by 5 (that gives 20%). 5% is half of 10%.
  • Writing 6% as the multiplier 0.6 instead of 0.06.
  • Finding the percentage but forgetting to add it on or take it off.
  • Using 0.15 instead of 0.85 to decrease by 15%.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out 10% of 340.

Answer: 34

Working: 340 ÷ 10 = 34.

Question 2. Without a calculator, work out 15% of 60.

Answer: 9

Working: 10% = 6, 5% = 3, so 15% = 9.

Question 3. Work out 35% of 280.

Answer: 98

Working: 0.35 × 280 = 98.

Related lessons

Continue in the full course

This lesson is section 4.7 (EGCMF0407) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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