Percentages · Year 8
In Percentages (Year 8) you practise 4 skills: A percentage of an amount, and a part as a percentage · Percentage increase and decrease · Comparing percentages · Percentage word problems. Percent means out of a hundred. 25% is 25/100, which is a quarter. To find 25% of 200, split 200 into four equal parts: each part is 50.
After an increase of 20%, the new price is 120% of the old price, so you multiply by 1.2. With 20% off, you pay 80% of the price, so you multiply by 0.8. When there are two changes one after the other, the second change is worked out from the new amount. An increase of 10% followed by a decrease of 10% does not take you back to the starting price: from 100 you go up to 110, then down to 99. To find the price before a change, write an equation. If you pay 80 after 20% off, then the price times 0.8 equals 80, so the price is 100.
Tip: If you are not sure, suppose the amount at the start is 100: then it is easy to see what it is now.
What you learn
A percentage of an amount, and a part as a percentage
For example: What is 10% of 390?
Answer and solution
The answer: 39
10% = 1/10 390 ÷ 10 = 39 10% of 390 is 39.
Percentage increase and decrease
For example: A hat cost £80, and its price went up by 5%. What is the new price?
Answer and solution
The answer: £84
The increase is 5% of 80: 5% = 1/20 80 ÷ 20 = 4 80 + 4 = 84 The new price is £84.
Comparing percentages
For example: Which is greater: 75% of 100, or 10% of 180?
- The second is greater
- They are equal
- The first is greater
Answer and solution
The answer: The first is greater
75% of 100: 75% = 3/4 100 ÷ 4 = 25 25 × 3 = 75 10% of 180: 10% = 1/10 180 ÷ 10 = 18 75 is greater than 18, so the first is greater.
Percentage word problems
For example: The price of a cinema ticket went up by 50%, and a ticket now costs £72. What was the price before the increase?
Answer and solution
The answer: £48
An increase of 50% means multiplying by 1.5. Call the old price x and write an equation: 1.5x = 72 Divide both sides by 1.5: x = 72 ÷ 1.5 = 48 The old price was £48.
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).