Year 6: Percentages in real life
Part of the Year 6 percentages chapter. Chapter overview · whole chapter on one page
Percentages in real life
Percentages are used everywhere: on phone batteries, in test results, in sales and in surveys. In each of these, the question is always the same: what part of the whole is it?
Start with a fraction (the part out of the whole). Then make the bottom number 100, or divide to find a decimal and multiply by 100. The answer is the percentage. Look at the units too: 90 minutes is 90 out of 120 minutes in a 2-hour film, not 90 out of 2.
Key ideas
- A percentage is always a part out of 100.
- To write a part as a percentage of a whole: part ÷ whole, then × 100.
- Make the units the same before you divide. 50 cm is 0.5 m, and 15 minutes is 15 out of 60 minutes.
- Some common results to know: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/10 = 10%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 4.
- Make the bottom number 100. 25 × 4 = 100, so multiply the top and the bottom by 4.18/25 = 72/100
- Read the top number as per cent. Out of 100 means per cent.72/100 = 72%
- Write the answer. 72
Check. 72% ÷ 100 = 0.72, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.15 ÷ 60 = 0.25
- Multiply the decimal by 100. That turns the decimal into per cent.0.25 × 100 = 25
- Write the answer. 25
Check. 25% ÷ 100 = 0.25, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 5.
- Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.15/20 = 75/100
- Read the top number as per cent. Out of 100 means per cent.75/100 = 75%
- Write the answer. 75
Check. 75% ÷ 100 = 0.75, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Watch out
Check the bottom number first. 15 minutes out of 60 minutes is the right fraction. 15 out of 60 is not the same as 15 out of 15.
Exam tip
Grown-up tip. Ask: “What is the whole?” Many children can find the part, but they put it on the wrong side.
Exercise 6B Percentages in real-life contexts
Non-calculatorKey words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 25.
- Make the bottom number 100. 4 × 25 = 100, so multiply the top and the bottom by 25.3/4 = 75/100
- Read the top number as per cent. Out of 100 means per cent.75/100 = 75%
- Write the answer. 75
Check. 75% ÷ 100 = 0.75, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.6 ÷ 30 = 0.2
- Multiply the decimal by 100. That turns the decimal into per cent.0.2 × 100 = 20
- Write the answer. 20
Check. 20% ÷ 100 = 0.2, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.6
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.6 × 100 = 60
- Write the answer as a percentage. So the decimal is this many out of 100.60
Check. 60% ÷ 100 = 0.6. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.90 ÷ 120 = 0.75
- Multiply the decimal by 100. That turns the decimal into per cent.0.75 × 100 = 75
- Write the answer. 75
Check. 75% ÷ 100 = 0.75, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Make the units the same, then write the part out of the whole.
- Change the units. 1 metre is 100 centimetres, so 2 metres is 200 centimetres.2 m = 200 cm
- Write the part as a fraction of the whole. The part is 50 cm and the whole is 200 cm.50/200
- Divide the top by the bottom. A fraction bar means divide.50 ÷ 200 = 0.25
- Multiply by 100. That gives the number of per cent.0.25 × 100 = 25
- Write the answer. 25
Check. 25% of 200 cm is 50 cm. ✓
Watch out. Do not divide 50 by 2. The whole rope is 200 cm, not 2 cm.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.7 ÷ 35 = 0.2
- Multiply the decimal by 100. That turns the decimal into per cent.0.2 × 100 = 20
- Write the answer. 20
Check. 20% ÷ 100 = 0.2, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 5.
- Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.17/20 = 85/100
- Read the top number as per cent. Out of 100 means per cent.85/100 = 85%
- Write the answer. 85
Check. 85% ÷ 100 = 0.85, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.120 ÷ 400 = 0.3
- Multiply the decimal by 100. That turns the decimal into per cent.0.3 × 100 = 30
- Write the answer. 30
Check. 30% ÷ 100 = 0.3, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.45
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.45 × 100 = 45
- Write the answer as a percentage. So the decimal is this many out of 100.45
Check. 45% ÷ 100 = 0.45. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 2.
- Make the bottom number 100. 50 × 2 = 100, so multiply the top and the bottom by 2.12/50 = 24/100
- Read the top number as per cent. Out of 100 means per cent.24/100 = 24%
- Write the answer. 24
Check. 24% ÷ 100 = 0.24, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.375
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.375 × 100 = 37.5
- Write the answer as a percentage. So the decimal is this many out of 100.37.5
Check. 37.5% ÷ 100 = 0.375. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Write the part as a fraction of the whole, then turn it into a percentage.
- Write the part as a fraction of the whole. The part goes on the top, and the whole goes on the bottom.1.25/5
- Divide the top by the bottom to get a decimal. A fraction bar means divide.1.25 ÷ 5 = 0.25
- Multiply the decimal by 100. That gives the number of per cent.0.25 × 100 = 25
- Write the answer. 25
Check. 25% of 5 is 1.25, which is 1.25. ✓
Watch out. The whole goes on the bottom. Make sure both numbers are in the same units first.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Write 3/4 as a decimal, then as a percentage, and compare with the other two.
- Write 3/4 as a decimal. 3 ÷ 4 = 0.75.3/4 = 0.75
- Write 0.75 as a percentage. Multiply by 100.0.75 × 100 = 75
- Compare the three forms. All three numbers describe the same part.3/4 = 0.75 = 75%
- Write the answer. Yes. 3/4 = 0.75 = 75%.
Check. Three quarters of anything is 75 out of 100. ✓
Watch out. Check each form by changing it into the others.
Key words. The part is the number we are interested in. The whole is the total. To write a part as a percentage of the whole, divide the part by the whole and then multiply by 100.
Method. Write 15 minutes as a fraction of an hour, then as a percentage.
- Write 15 minutes as a fraction of 60 minutes. An hour has 60 minutes.15/60
- Simplify the fraction. Divide the top and the bottom by 15.15 ÷ 15 = 1, 60 ÷ 15 = 4, so 1/4
- Write 1/4 as a percentage. Quarters are 25%.1/4 = 25%
- Write the answer. No. 15 minutes is 25% of an hour.
Check. 15 minutes is a quarter of an hour, and a quarter is 25%. ✓
Watch out. Ben has used 15 out of 100, not 15 out of 60. Always use the whole that the question is about.