Fractions and percentages
Percentages
Per cent means 'out of 100'. In this section we find percentages of whole numbers and of shapes, and use percentages to solve everyday problems like sales and pie charts.
What a percentage means
Per cent means 'out of 100'. So 30% means 30 out of every 100. We see percentages every day: a 70% test score, a 30% chance of rain, or '25% off' in a sale.
Find 10%, then build up
10% is one tenth, so to find 10% you divide by 10. You can find other percentages by scaling: - 20% is double 10% - 5% is half of 10% - so 15% = 10% + 5%. Remember to write the units in your answer.
Percentages of shapes and amounts
If 3 out of 10 equal parts of a shape are shaded, that is 30% (the same as 30 out of 100). To write one amount as a percentage of another, make a fraction and change it to hundredths: 5 cm out of 20 cm = 5/20 = 1/4 = 25%.
Increase, decrease and finding the whole
To INCREASE by a percentage, find the percentage and add it on. To DECREASE, subtract it. If you know what a percentage is worth, you can find 100%: if 40% = 32, then 10% = 8 and 100% = 80.
Worked examples
Finding 10% of a quantity
- 10% means one tenth, so divide by 10.
- 40 divided by 10 = 4.
Answer: 10% of 40 = 4
Finding 20% by scaling 10%
- First find 10% of 50: 50 divided by 10 = 5.
- 20% is double 10%, so 5 times 2 = 10.
Answer: 20% of 50 = 10
Finding a percentage using a 5% step
- Find 10% of 120: 120 divided by 10 = 12.
- Find 5% by halving 10%: 12 divided by 2 = 6.
- 15% = 10% + 5% = 12 + 6 = 18.
Answer: 15% of 120 = 18
What percentage of a shape is shaded
- The shape is split into 10 equal parts and 3 are shaded.
- 3 out of 10 is the same as 30 out of 100.
Answer: 3 out of 10 shaded = 30%
Writing one amount as a percentage of another
- Song cuts a 5 cm piece from a 20 cm strip.
- Write it as a fraction: 5 out of 20 = 5/20.
- 5/20 simplifies to 1/4, which is 25%.
Answer: 5 cm out of 20 cm = 25%
Percentage increase and decrease
- A $40 coat rises by 10%: 10% of 40 = 4, and 40 + 4 = 44.
- An $8 plant is 25% off: 25% of 8 = 2, and 8 - 2 = 6.
Answer: The coat becomes $44 and the plant becomes $6.
Finding the whole from a percentage
- 40% of the children is 32 children.
- Find 10%: 32 divided by 4 = 8.
- Multiply by 10 for 100%: 8 times 10 = 80.
Answer: If 40% = 32 children, then 100% = 80 children.
Where you see this in real life
- Working out the discount in a '25% off' sale.
- Reading a pie chart where 40% of children chose elephants.
- Scoring 70% in a maths test.
Key words
- Per cent
- Out of 100. The symbol % means per cent.
- Percentage
- A number written as a part out of 100, such as 30%.
- Operator
- A percentage or fraction used to find a part of a number, such as 20% of 50.
- Discount
- An amount taken off a price, often given as a percentage.