Mastering Maths: Percentages

By Team 11+ Connect

What does the word 'percentage' mean?

• 'cent' means '100'

• 'per' means 'out of'

• A percentage is therefore a way of working out the amount out of 100.

Key Percentages to Know

100%	100/out of 100	one whole
75%	75/out of 100	three quarters
50%	50/out of 100	one half
25%	25/out of 100	one quarter
10%	10/out of 100	one tenth

Top Tips for Percentage Questions

• To increase an amount by a percentage, you need to find the given percentage and add it to the original number.

• To decrease an amount by a percentage, you need to find the given percentage and subtract it from the original number.

• Percentage questions are all focused on something being divided by 100. For most 11+ percentage questions, you can work out the answer by finding 10% first.

The Power of 10%

Being able to find 10% is key to answering percentage questions. To find 10% of a number, all you need to do is divide it by 10. For example, 10% of 25 is 2.50. Once you have found 10%, it is easy to find other amounts:

• To work out 20% of 25, times 2.50 by 2

• To work out 30% of 25, times 2.50 by 3

• To work out 40% of 25, times 2.50 by 4

• To work out 60% of 25, times 2.50 by 6

Likewise, finding a smaller amount is easy too:

• To work out 5% of 25, divide 2.50 by 2

• To work out 1% of 25, divide 2.50 by 10

Questions

Percentages: Mental Arithmetic

1. 10% of 140

2. 20% of 50

3. 60% of 120

4. 75% of 80

5. 25% of 140

6. 45% of 320

Percentages: Word Problems

1. The price of a tennis racket has been reduced by 20%. The original price was £18. what is the reduced price of the tennis racket?

2. In a class full of 25 children, there are 15 boys and 10 girls. What percentage of the class are boys?

3. Robert has a basket full of fruit. He has 12 apples, 8 bananas and 10 peaches. What's the percentage of the apples?

4. Saira went shopping. She picked out three items: a top for £9, a dress for £12 and a pair of shoes for £15. All the items have an additional 10% off. How much does Saira spend in total?

Answers

Percentages: Mental Arithmetic

1. 10% of 140 = 14

2. 20% of 50 = 10

3. 60% of 120 = 72

4. 75% of 80 = 60

5. 25% of 140 = 35

6. 45% of 320 = 144

Percentages: Word Problems

1. £14.40

2. 60%

3. 40%

4. £32.40