Year 6 Percentages: worked examples and questions with answers

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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   3 ÷ 8 = 0.375
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.375 × 100 = 37.5
3. Write the answer.
   37.5

Check. 37.5% ÷ 100 = 0.375, which is the same as the fraction we started with. ✓

Watch out. Multiply by 100 at the end, not at the start.

Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.

Method. Change each number to a decimal or to a percentage, then compare.

1. Write 4/10 as a decimal. Divide 4 by 10.
   4/10 = 0.4
2. Write 40% as a decimal. 40 out of 100 is 40/100.
   40% = 0.4
3. Write 4% and 0.04 as decimals. 4% is 4/100, which is 0.04.
   4% = 0.04, and 0.04 is not 0.4
4. Write 2/5 as a decimal. Divide 2 by 5.
   2/5 = 0.4
5. Write the answer. Three numbers are equal to 0.4.
   4/10, 40%, 2/5

Check. 0.4 = 4/10 = 40% = 2/5. ✓

Watch out. 4% and 0.04 look like 40% and 0.4, but they are ten times smaller.

Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.

Method. Write every number as a decimal, then put the decimals in order.

1. Write each number as a decimal. Percentages become decimals by dividing by 100.
   0.3, 35% = 0.35, 1/4 = 0.25, 0.22
2. Order the decimals, smallest first. Compare the tenths, then the hundredths.
   0.22 < 0.25 < 0.3 < 0.35
3. Write the answer in the original forms. Keep each number as it was written.
   0.22, 1/4, 0.3, 35%

Check. 0.22 is 22%, 1/4 is 25%, 0.3 is 30% and 35% is 35%. ✓

Watch out. Do not compare 35 with 3 and 22 by their digits. Put them all into the same form first.

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 1/8 to a decimal, then to a percentage, and compare with 18%.

1. Write 1/8 as a decimal. 1 ÷ 8 = 0.125.
   1 ÷ 8 = 0.125
2. Write 0.125 as a percentage. Multiply by 100.
   0.125 × 100 = 12.5
3. Compare with 18%. 12.5% is not the same as 18%.
   12.5% ≠ 18%
4. Write the answer.
   No. 1/8 = 0.125 = 12.5%.

Check. 1/8 is one eighth, which is a little more than 1/10 (10%). ✓

Watch out. 1/8 is a little more than 10%, not nearly 20%.

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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.125
2. Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.
   0.125 × 100 = 12.5
3. Write the answer as a percentage. So the decimal is this many out of 100.
   12.5

Check. 12.5% ÷ 100 = 0.125. ✓

Watch out. Do not forget the step. 0.7 is 70%, not 7%.

Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.

Method. Compare the two numbers in the same form.

1. Write 3/8 as a decimal. 3 divided by 8.
   3/8 = 0.375
2. Write 0.375 as a percentage. Multiply by 100.
   0.375 × 100 = 37.5
3. Compare with 37%. 37.5% is more than 37%, so 37% is not the same.
   37.5% ≠ 37%
4. Write the answer.
   No. 3/8 = 0.375 = 37.5%, not 37%.

Check. 37% = 0.37, which is less than 0.375. ✓

Watch out. Look at the hundredths: 0.37 and 0.375 are different.

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 25.

1. Make the bottom number 100. 4 × 25 = 100, so multiply the top and the bottom by 25.
   3/4 = 75/100
2. Read the top number as per cent. Out of 100 means per cent.
   75/100 = 75%
3. 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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   6 ÷ 30 = 0.2
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.2 × 100 = 20
3. 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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.6
2. 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
3. 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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   90 ÷ 120 = 0.75
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.75 × 100 = 75
3. 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.

1. Change the units. 1 metre is 100 centimetres, so 2 metres is 200 centimetres.
   2 m = 200 cm
2. Write the part as a fraction of the whole. The part is 50 cm and the whole is 200 cm.
   50/200
3. Divide the top by the bottom. A fraction bar means divide.
   50 ÷ 200 = 0.25
4. Multiply by 100. That gives the number of per cent.
   0.25 × 100 = 25
5. 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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   7 ÷ 35 = 0.2
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.2 × 100 = 20
3. 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.

1. Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.
   17/20 = 85/100
2. Read the top number as per cent. Out of 100 means per cent.
   85/100 = 85%
3. 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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   120 ÷ 400 = 0.3
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.3 × 100 = 30
3. 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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.45
2. 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
3. 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.

1. Make the bottom number 100. 50 × 2 = 100, so multiply the top and the bottom by 2.
   12/50 = 24/100
2. Read the top number as per cent. Out of 100 means per cent.
   24/100 = 24%
3. 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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.375
2. 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
3. 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.

1. 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
2. Divide the top by the bottom to get a decimal. A fraction bar means divide.
   1.25 ÷ 5 = 0.25
3. Multiply the decimal by 100. That gives the number of per cent.
   0.25 × 100 = 25
4. 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.

1. Write 3/4 as a decimal. 3 ÷ 4 = 0.75.
   3/4 = 0.75
2. Write 0.75 as a percentage. Multiply by 100.
   0.75 × 100 = 75
3. Compare the three forms. All three numbers describe the same part.
   3/4 = 0.75 = 75%
4. 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.

1. Write 15 minutes as a fraction of 60 minutes. An hour has 60 minutes.
   15/60
2. Simplify the fraction. Divide the top and the bottom by 15.
   15 ÷ 15 = 1, 60 ÷ 15 = 4, so 1/4
3. Write 1/4 as a percentage. Quarters are 25%.
   1/4 = 25%
4. 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.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. 10% is one tenth, so divide by 10.

1. Write 10% as a fraction. 10 out of 100 is one tenth.
   10% = 10/100 = 1/10
2. Divide the amount by 10. One tenth of the amount is found by dividing by 10.
   250 ÷ 10 = 25
3. Write the answer. The answer is smaller than the amount.
   25

Check. 25 × 10 = 250. ✓

Watch out. 10% of 50 is 5, not 40. Dividing by 10 is not the same as taking 10 away.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. 25% is one quarter, so divide the amount by 4.

1. Write 25% as a fraction. 25 out of 100 is one quarter.
   25% = 1/4
2. Divide the amount by 4. One quarter means one of four equal parts.
   640 ÷ 4 = 160
3. Write the answer.
   160

Check. 160 × 4 = 640. ✓

Watch out. 25% is a quarter, not a half. Divide by 4, not by 2.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. 50% is one half, so divide the amount by 2.

1. Write 50% as a fraction. 50 out of 100 is one half.
   50% = 1/2
2. Halve the amount. Dividing by 2 finds one half.
   12 ÷ 2 = 6
3. Write the answer.
   6

Check. 6 + 6 = 12, so two halves make the whole. ✓

Watch out. Halving is quick for 50%. For 25%, halve twice, or divide by 4.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. First find the part that is given away, then take it from the total.

1. Find 25% of the total. This is the part that is given away.
   25% of 80 = 20
2. Take that part away from the total. What is left is the rest.
   80 − 20 = 60
3. Write the answer.
   60

Check. 20 + 60 = 80. ✓

Watch out. Two steps: first find the part, then take it away. Do not stop after the first step.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% by dividing the amount by 100.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   1% = 1/100
2. Find 1% of 3600. Divide by 100, because 1% is one hundredth.
   3600 ÷ 100 = 36
3. Write the answer.
   36

Check. 36 is less than 3600, because 1% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 1 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find one quarter first, then take three of those quarters.

1. Write 75% as a fraction. 75 out of 100 is 3 quarters, because 25% is 1/4.
   75% = 3/4
2. Find one quarter: divide by 4. One quarter is 25%.
   120 ÷ 4 = 30
3. Multiply by 3. Three quarters is three lots of one quarter.
   30 × 3 = 90
4. Write the answer.
   90

Check. 90 is less than 120, because 75% is less than 100%. ✓

Watch out. Do not find 25% and stop. The question asks for 75%, so take three quarters.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% of 500 and 1% of 5000, and compare the answers.

1. Find 10% of 500. 10% is one tenth, so divide by 10.
   500 ÷ 10 = 50
2. Find 1% of 5000. 1% is one hundredth, so divide by 100.
   5000 ÷ 100 = 50
3. Compare. The two answers are the same.
   50 = 50
4. Write the answer.
   Yes. Both are 50.

Check. 10% of 500 is 50 and 1% of 5000 is 50. ✓

Watch out. The percentages are different, but the amounts are not. Work out both before you decide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out each side, then compare.

1. Find 50% of 60. Halve 60.
   60 ÷ 2 = 30
2. Find 25% of 120. Divide by 4.
   120 ÷ 4 = 30
3. Compare. The two answers are the same.
   30 = 30
4. Write the answer.
   Yes. Both are 30.

Check. 50% and 25% are not the same, but 60 and 120 are different amounts. ✓

Watch out. A bigger percentage of a smaller amount can equal a smaller percentage of a bigger amount.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 35.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   35% = 35/100
2. Find 1% of 240. Divide by 100, because 1% is one hundredth.
   240 ÷ 100 = 2.4
3. Multiply by 35. 35% is 35 lots of 1%.
   2.4 × 35 = 84
4. Write the answer.
   84

Check. 84 is less than 240, because 35% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 15.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   15% = 15/100
2. Find 1% of 2000. Divide by 100, because 1% is one hundredth.
   2000 ÷ 100 = 20
3. Multiply by 15. 15% is 15 lots of 1%.
   20 × 15 = 300
4. Write the answer.
   300

Check. 300 is less than 2000, because 15% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 15 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 40.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   40% = 40/100
2. Find 1% of 3.5. Divide by 100, because 1% is one hundredth.
   3.5 ÷ 100 = 0.035
3. Multiply by 40. 40% is 40 lots of 1%.
   0.035 × 40 = 1.4
4. Write the answer.
   1.4

Check. 1.4 is less than 3.5, because 40% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 40 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 15.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   15% = 15/100
2. Find 1% of 6.4. Divide by 100, because 1% is one hundredth.
   6.4 ÷ 100 = 0.064
3. Multiply by 15. 15% is 15 lots of 1%.
   0.064 × 15 = 0.96
4. Write the answer.
   0.96

Check. 0.96 is less than 6.4, because 15% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 15 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 35.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   35% = 35/100
2. Find 1% of 80. Divide by 100, because 1% is one hundredth.
   80 ÷ 100 = 0.8
3. Multiply by 35. 35% is 35 lots of 1%.
   0.8 × 35 = 28
4. Write the answer.
   28

Check. 28 is less than 80, because 35% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% first, then add the 5% and 1% parts that make up 20%.

1. Split 20% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.
   20% = 2 lots of 10%
2. Find 10% of 300, then 2 lots. 10% is one tenth, so divide by 10.
   10% of 300 = 30; 2 × 30 = 60
3. Add the parts. Add the answers for each part to find the whole percentage.
   60 = 60

Check. Fraction check: 20/100 × 300 = 60. ✓

Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 6.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   6% = 6/100
2. Find 1% of 2.5. Divide by 100, because 1% is one hundredth.
   2.5 ÷ 100 = 0.025
3. Multiply by 6. 6% is 6 lots of 1%.
   0.025 × 6 = 0.15
4. Write the answer.
   0.15

Check. 0.15 is less than 2.5, because 6% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 6 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out each person’s answer, then decide.

1. Ali: find 15% of 200. 10% is 20 and 5% is half of 20, which is 10.
   20 + 10 = 30, so 15% of 200 = 30
2. Bea: find 20% of 150. 10% is 15, so 20% is two lots of 15.
   15 + 15 = 30, so 20% of 150 = 30
3. Compare. Both answers are 30.
   30 = 30
4. Write the answer.
   Both are right.

Check. Both people found 30. ✓

Watch out. Two different calculations can give the same answer.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out each side, then compare.

1. Find 25% of 80. One quarter of 80 is 80 ÷ 4.
   80 ÷ 4 = 20
2. Find 80% of 25. 80% is 80 lots of 1%. 1% of 25 is 0.25, so 80 lots is 80 × 0.25.
   80 × 0.25 = 20
3. Compare. The two answers are the same.
   20 = 20
4. Write the answer.
   No. They are both 20, so Ben is not right.

Check. Ben thought 25% of 80 was more than 80% of 25. Both are 20. ✓

Watch out. A percentage of a number and the same percentage of the other way round are equal.

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. Change each to a percentage, then compare.

1. Write 3/5 as a percentage. 3 out of 5 is 60%.
   3/5 = 60%
2. Compare with 58%. 60% is more than 58%.
   60% > 58%
3. Write the answer.
   3/5

Check. 3/5 is 60%, and 60% is more than 58%. ✓

Watch out. Change the fraction to a percentage before you compare.

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. Change both to percentages, then compare.

1. Write 3/4 as a percentage. 3 quarters is 75%.
   3/4 = 75%
2. Compare with 70%. 75% is more than 70%.
   75% > 70%
3. Write the answer.
   3/4

Check. 3/4 of a cake is more than 70% of a cake. ✓

Watch out. 3/4 and 70% both describe parts of a cake, so compare them as percentages.

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. Change each one to a percentage out of 100, then compare.

1. Change 18 out of 25 to a percentage. 18/25 = 0.72, and 0.72 × 100 = 72.
   18/25 = 72%
2. Change 33 out of 40 to a percentage. 33 ÷ 40 = 0.825, and 0.825 × 100 = 82.5.
   33/40 = 82.5%
3. Compare the two percentages. Both are out of 100, so the bigger number is the bigger share.
   72% < 82.5%
4. Write the answer.
   Ben did better (82.5% against 72%).

Check. 82.5% is more than 72%, so Ben did better. ✓

Watch out. Compare percentages, not the numbers on top. 18 is more than 15, but 15 out of 20 is the bigger share.

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. Find each amount as a percentage of 250 or 120, then compare the amounts.

1. Find 20% of 250. 1% of 250 is 2.5, so 20% is 20 lots of 2.5.
   20% of 250 = 50
2. Find 35% of 120. 1% of 120 is 1.2, so 35% is 35 lots of 1.2.
   35% of 120 = 42
3. Compare. 50 is more than 42.
   50 > 42
4. Write the answer.
   20% of 250 (which is 50)

Check. 50 is more than 42, so 20% of 250 is the bigger amount. ✓

Watch out. Do not compare 20 with 35. Find both amounts first.

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. Find the saving in pounds for each coat, then compare.

1. Find the saving at Shop X: 25% of £60. 1% of £60 is £0.60, so 25% is 25 lots of that. Or divide by 4.
   60 ÷ 4 = 15
2. Find the saving at Shop Y. Shop Y takes £14 off.
   Saving = 14
3. Compare. The bigger saving is better.
   15 > 14
4. Write the answer.
   Shop X

Check. Shop X saves £15 and Shop Y saves £14. ✓

Watch out. The coat prices are different, so compare the savings, not the percentages.

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. Find each saving in pounds, then compare.

1. Find the saving at Shop P: 30% of £20. Divide 20 by 100, then multiply by 30.
   30% of 20 = 6
2. Find the saving at Shop Q: a quarter of £24. A quarter is 25%, so divide by 4.
   24 ÷ 4 = 6
3. Compare. Both savings are the same.
   6 = 6
4. Write the answer.
   They are the same: £6 each.

Check. Both shops take £6 off. ✓

Watch out. Equal savings are possible even with different percentages and prices.

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. Change each year group to a percentage, then compare.

1. Year 4: 24 out of 60. 24 ÷ 60 = 0.4, which is 40%.
   24/60 = 40%
2. Year 5: 27 out of 75. 27 ÷ 75 = 0.36, which is 36%.
   27/75 = 36%
3. Compare. 40% is more than 36%.
   40% > 36%
4. Write the answer.
   Year 4 (40% against 36%).

Check. Year 4 has the bigger percentage, although Year 5 has more pupils who like cats. ✓

Watch out. Compare the percentages, not the numbers of pupils.

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. Find how many European stamps each person has, then compare the numbers.

1. Find 40% of Ella’s 150 stamps. 1% of 150 is 1.5, so 40% is 40 lots of 1.5.
   40% of 150 = 60
2. Find 45% of Jack’s 120 stamps. 1% of 120 is 1.2, so 45% is 45 lots of 1.2.
   45% of 120 = 54
3. Compare the numbers of stamps. Compare the amounts, because both are amounts of stamps.
   60 > 54
4. Write the answer.
   Ella has more European stamps (60 against 54).

Check. Ella has 60 and Jack has 54. Jack’s percentage is bigger, but he has fewer stamps. ✓

Watch out. Here the question asks for an amount, so compare the amounts, not the percentages.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out each side as an amount, then compare.

1. Find 30% of 200. 1% of 200 is 2, so 30% is 30 lots of 2.
   30% of 200 = 60
2. Find 25% of 250. 1% of 250 is 2.5, so 25% is 25 lots of 2.5.
   25% of 250 = 62.5
3. Compare. 62.5 is more than 60.
   62.5 > 60
4. Write the answer.
   No. 25% of 250 = 62.5, which is more than 60.

Check. The percentage is smaller, but the amount is bigger. ✓

Watch out. A smaller percentage of a bigger amount can be the bigger answer.

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. Change the fraction to a percentage, then compare with 85%.

1. Write 7/8 as a decimal. 7 ÷ 8 = 0.875.
   7/8 = 0.875
2. Write 0.875 as a percentage. Multiply by 100.
   0.875 × 100 = 87.5
3. Compare with 85%. 87.5% is more than 85%.
   87.5% > 85%
4. Write the answer.
   Yes. 7/8 = 87.5%, which is more than 85%.

Check. Each eighth is 12.5%, so 7 eighths is 87.5%. ✓

Watch out. Eighths are not in tenths or quarters, so change them to a decimal first.

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. Change each class to a percentage, then compare.

1. Class of 40: 12 left-handed. 12 out of 40.
   12/40 = 30%
2. Class of 25: 8 left-handed. 8 out of 25.
   8/25 = 32%
3. Compare. 32% is more than 30%.
   32% > 30%
4. Write the answer.
   The class of 25 (32% against 30%).

Check. The smaller class has the bigger percentage. ✓

Watch out. Look at the percentages, not at the size of the class.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Replace the numbers with easier ones, work out the estimate, then check it.

1. Use easier numbers. 52% is about 50%, and 398 is about 400.
   52% ≈ 50%, 398 ≈ 400
2. Work out 50% of 400. 50% of 400 is easy to find.
   50% of 400 = 200
3. Write the estimate. The answer is about this size.
   200
4. Check with the exact value. The exact answer is 206.96, which is close to the estimate.
   52% of 398 = 206.96

Check. The estimate 200 and the exact answer 206.96 are close. ✓

Watch out. An estimate tells you if an answer is sensible. It does not replace the exact answer.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Use 25% of 48 as an estimate for 24% of 49.

1. Use easier numbers. 24% is about 25%, and 49 is about 48.
   24% ≈ 25%, 49 ≈ 48
2. Work out 25% of 48. 25% is one quarter, so divide by 4.
   48 ÷ 4 = 12
3. Write the estimate. The answer is about this size.
   12
4. Check with the exact value. The exact answer is 11.76, which is close to 12.
   24% of 49 = 11.76

Check. 12 and 11.76 are close. ✓

Watch out. The estimate is close, but it is not exact. Use it to check, not to finish the question.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out 40% of 150, then compare it with 65.

1. Find 40% of 150. 1% of 150 is 1.5, so 40% is 40 lots of 1.5.
   40% of 150 = 60
2. Compare with 65. 60 is less than 65.
   60 < 65
3. Write the answer.
   Less (40% of 150 is 60).

Check. 60 is 5 less than 65. ✓

Watch out. Find the amount first. Then compare it with the number in the question.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 25% of the price, then take it from the price.

1. Find 25% of the total. This is the part that is given away.
   25% of 64 = 16
2. Take that part away from the total. What is left is the rest.
   64 − 16 = 48
3. Write the answer.
   48

Check. 16 + 48 = 64. ✓

Watch out. Two steps: first find the part, then take it away. Do not stop after the first step.

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. Find how many walk, then the rest, then 40% of the rest.

1. Find the pupils who walk. 25% is a quarter, so divide by 4.
   240 ÷ 4 = 60 walk
2. Find the pupils who do not walk. Take the walkers from the whole school.
   240 - 60 = 180
3. Find 40% of the 180. 1% of 180 is 1.8, so 40% is 40 lots of 1.8.
   40% of 180 = 72
4. Write the answer.
   72

Check. 60 + 180 = 240, and 72 is less than 180. ✓

Watch out. The 40% is of the pupils who do not walk, not of the whole school.

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. Find 1% of the whole first, then multiply by 100 to find the whole.

1. Write what we know. 30% of the whole amount is 45.
   30% → 45
2. Find 1%. Divide the part by 30, because 30% is 30 lots of 1%.
   45 ÷ 30 = 1.5
3. Find 100%. The whole is 100%, so multiply the 1% amount by 100.
   1.5 × 100 = 150
4. Write the answer.
   150

Check. 30% of 150 is 45, which matches the part of 45 in the question. ✓

Watch out. Do not find 30% of 45. The 45 is the part, and we need the whole.

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. Find 1% of the whole first, then multiply by 100 to find the whole.

1. Write what we know. 15% of the whole amount is 12.
   15% → 12
2. Find 1%. Divide the part by 15, because 15% is 15 lots of 1%.
   12 ÷ 15 = 0.8
3. Find 100%. The whole is 100%, so multiply the 1% amount by 100.
   0.8 × 100 = 80
4. Write the answer.
   80

Check. 15% of 80 is 12, which matches the part of 12 in the question. ✓

Watch out. Do not find 30% of 45. The 45 is the part, and we need the whole.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find how much Ben has saved, then take it from the price.

1. Find 60% of £220. 10% is £22, so 60% is 6 lots of £22.
   6 × 22 = 132
2. Find how much more he needs. Take what he has saved from the price.
   220 - 132 = 88
3. Write the answer.
   88

Check. 132 + 88 = 220. ✓

Watch out. Find how much he has saved first. The question asks how much more he needs.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% first, then add the 5% and 1% parts that make up 4%.

1. Split 4% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.
   4% = 4 lots of 1%
2. Find 1% of 350, then 4 lots. Divide by 100 for 1%.
   1% of 350 = 3.5; 4 × 3.5 = 14
3. Add the parts. Add the answers for each part to find the whole percentage.
   14 = 14

Check. Fraction check: 4/100 × 350 = 14. ✓

Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 35% of 60 by building it from 10%, then check Tom’s answer.

1. Find 10% of 60. 10% is one tenth, so divide by 10.
   60 ÷ 10 = 6
2. Find 30% of 60. 30% is three lots of 10%.
   3 × 6 = 18
3. Find 5% of 60. Half of 10% is 5%.
   6 ÷ 2 = 3
4. Add to find 35%. 35% is 30% plus 5%.
   18 + 3 = 21
5. Write the answer. Tom is not right. Tom found 30%, not 35%.
   No, 35% of 60 is 21.

Check. 35% of 60 = 21. ✓

Watch out. 18 is 30% of 60. Check every part of the percentage, not just the tens.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find each part, then add and compare.

1. Find 50% of 80. Half of 80.
   80 ÷ 2 = 40
2. Find 10% of 80. 10% is one tenth.
   80 ÷ 10 = 8
3. Add the two parts. Add the 50% and the 10% to find 60%.
   40 + 8 = 48
4. Find 60% of 80 to compare. 60% is 6 lots of 10%.
   6 × 8 = 48
5. Write the answer. The two answers are the same.
   Yes. 48 = 48.

Check. 50% + 10% = 60%, so the two ways give the same answer. ✓

Watch out. Percentages can be added when they are of the same amount.

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. Try a number, then decide.

1. Try 10. Choose an easy positive number.
   10
2. Find 60% of 10. Half of 10 is 5. 60% is more than 50%.
   60% of 10 = 6
3. Compare with half. 6 is more than 5, which is half of 10.
   6 > 5
4. Decide for every positive number. Any positive number gives the same result, because 60% is more than 50%.
   Always (for any number above 0).

Check. Try 20: 60% of 20 = 12, which is more than 10. ✓

Watch out. Half of a number is 50%. Compare every percentage with 50%.

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. Work out the sales on each day, one after the other.

1. Sold on Monday: 25% of 480. 25% is a quarter, so divide by 4.
   480 ÷ 4 = 120
2. Left after Monday. Take Monday’s sales from the total.
   480 - 120 = 360
3. Sold on Tuesday: a third of 360. A third is 360 ÷ 3.
   360 ÷ 3 = 120
4. Left after Tuesday. Take Tuesday’s sales from what was left.
   360 - 120 = 240
5. Write the answer.
   240

Check. 120 + 120 + 240 = 480. ✓

Watch out. Each day is worked out from what is left, not from the original 480.

Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.

Method. Divide the percentage by 100 to get a decimal.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   65% = 65/100
2. Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.
   65 ÷ 100 = 0.65
3. Write the answer. Use a zero to hold a place if one is needed.
   0.65

Check. 0.65 × 100 = 65, so the decimal is 65%. ✓

Watch out. 65% is not 65. Divide by 100 first; 5% is 0.05, not 0.5.

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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.04
2. Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.
   0.04 × 100 = 4
3. Write the answer as a percentage. So the decimal is this many out of 100.
   4

Check. 4% ÷ 100 = 0.04. ✓

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.

1. Divide the top number by the bottom number. A fraction bar means divide.
   5 ÷ 8 = 0.625
2. Multiply the decimal by 100. That turns the decimal into per cent.
   0.625 × 100 = 62.5
3. Write the answer.
   62.5

Check. 62.5% ÷ 100 = 0.625, 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.

1. Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.
   3/20 = 15/100
2. Read the top number as per cent. Out of 100 means per cent.
   15/100 = 15%
3. Write the answer.
   15

Check. 15% ÷ 100 = 0.15, which is the same as the fraction we started with. ✓

Watch out. Multiply by 100 at the end, not at the start.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. 10% is one tenth, so divide by 10.

1. Write 10% as a fraction. 10 out of 100 is one tenth.
   10% = 10/100 = 1/10
2. Divide the amount by 10. One tenth of the amount is found by dividing by 10.
   470 ÷ 10 = 47
3. Write the answer. The answer is smaller than the amount.
   47

Check. 47 × 10 = 470. ✓

Watch out. 10% of 50 is 5, not 40. Dividing by 10 is not the same as taking 10 away.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% by dividing the amount by 100.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   1% = 1/100
2. Find 1% of 900. Divide by 100, because 1% is one hundredth.
   900 ÷ 100 = 9
3. Write the answer.
   9

Check. 9 is less than 900, because 1% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 1 before you divide.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% first, then add the 5% and 1% parts that make up 15%.

1. Split 15% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.
   15% = 1 lot of 10% + 5%
2. Find 10% of 360, then 1 lot. 10% is one tenth, so divide by 10.
   10% of 360 = 36; 1 × 36 = 36
3. Find 5%. Half of 10% is 5%, so halve the 10% answer.
   5% of 360 = 36 ÷ 2 = 18
4. Add the parts. Add the answers for each part to find the whole percentage.
   36 + 18 = 54

Check. Fraction check: 15/100 × 360 = 54. ✓

Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 1% first by dividing by 100, then multiply by 35.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   35% = 35/100
2. Find 1% of 80. Divide by 100, because 1% is one hundredth.
   80 ÷ 100 = 0.8
3. Multiply by 35. 35% is 35 lots of 1%.
   0.8 × 35 = 28
4. Write the answer.
   28

Check. 28 is less than 80, because 35% is less than 100%. ✓

Watch out. Dividing by 100 gives 1%. Do not multiply by 35 before you divide.

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. Change both to percentages, then compare.

1. Write 3/4 as a percentage. 3 quarters is 75%.
   3/4 = 75%
2. Compare with 72%. 75% is more than 72%.
   75% > 72%
3. Write the answer.
   3/4

Check. 3/4 is 75%, which is more than 72%. ✓

Watch out. Change the fraction to a percentage before you compare.

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. Change Mia’s score to a percentage, then compare with Liam’s 70%.

1. Change 16 out of 25 to a percentage. 16 ÷ 25 = 0.64, and 0.64 × 100 = 64.
   16/25 = 64%
2. Compare with 70%. Both are out of 100, so the bigger number is the bigger percentage.
   64% < 70%
3. Write the answer.
   Liam (70% against 64%).

Check. Mia scored 64% and Liam scored 70%. ✓

Watch out. Do not compare 16 with 70. Change Mia’s score to a percentage first.

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.

1. Write the decimal. Read the decimal carefully, with its point.
   0.9
2. Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.
   0.9 × 100 = 90
3. Write the answer as a percentage. So the decimal is this many out of 100.
   90

Check. 90% ÷ 100 = 0.9. ✓

Watch out. Do not forget the step. 0.7 is 70%, not 7%.

Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.

Method. Divide the percentage by 100 to get a decimal.

1. Write the percentage as a fraction out of 100. Per cent means out of 100.
   45% = 45/100
2. Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.
   45 ÷ 100 = 0.45
3. Write the answer. Use a zero to hold a place if one is needed.
   0.45

Check. 0.45 × 100 = 45, so the decimal is 45%. ✓

Watch out. 45% is not 45. Divide by 100 first; 5% is 0.05, not 0.5.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find one quarter first, then take three of those quarters.

1. Write 75% as a fraction. 75 out of 100 is 3 quarters, because 25% is 1/4.
   75% = 3/4
2. Find one quarter: divide by 4. One quarter is 25%.
   64 ÷ 4 = 16
3. Multiply by 3. Three quarters is three lots of one quarter.
   16 × 3 = 48
4. Write the answer.
   48

Check. 48 is less than 64, because 75% is less than 100%. ✓

Watch out. Do not find 25% and stop. The question asks for 75%, so take three quarters.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% first, then add the 5% and 1% parts that make up 35%.

1. Split 35% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.
   35% = 3 lots of 10% + 5%
2. Find 10% of 260, then 3 lots. 10% is one tenth, so divide by 10.
   10% of 260 = 26; 3 × 26 = 78
3. Find 5%. Half of 10% is 5%, so halve the 10% answer.
   5% of 260 = 26 ÷ 2 = 13
4. Add the parts. Add the answers for each part to find the whole percentage.
   78 + 13 = 91

Check. Fraction check: 35/100 × 260 = 91. ✓

Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Find 10% first, then add the 5% and 1% parts that make up 15%.

1. Split 15% into 10%, 5% and 1% parts. Ten, five and one make the parts we can find easily.
   15% = 1 lot of 10% + 5%
2. Find 10% of 40, then 1 lot. 10% is one tenth, so divide by 10.
   10% of 40 = 4; 1 × 4 = 4
3. Find 5%. Half of 10% is 5%, so halve the 10% answer.
   5% of 40 = 4 ÷ 2 = 2
4. Add the parts. Add the answers for each part to find the whole percentage.
   4 + 2 = 6

Check. Fraction check: 15/100 × 40 = 6. ✓

Watch out. Check the parts: 10% is a tenth, so divide by 10. 1% is divide by 100.

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.

1. Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.
   7/20 = 35/100
2. Read the top number as per cent. Out of 100 means per cent.
   35/100 = 35%
3. Write the answer.
   35

Check. 35% ÷ 100 = 0.35, 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 4.

1. Make the bottom number 100. 25 × 4 = 100, so multiply the top and the bottom by 4.
   14/25 = 56/100
2. Read the top number as per cent. Out of 100 means per cent.
   56/100 = 56%
3. Write the answer.
   56

Check. 56% ÷ 100 = 0.56, which is the same as the fraction we started with. ✓

Watch out. Multiply by 100 at the end, not at the start.

Key words. Of means multiply. So 15% of 360 means 15% × 360. To find a percentage of an amount, write the percentage as a fraction out of 100 and multiply.

Method. Work out each amount, then compare.

1. Find 40% of 150. 1% of 150 is 1.5, so 40% is 40 lots of 1.5.
   40% of 150 = 60
2. Find 60% of 90. 1% of 90 is 0.9, so 60% is 60 lots of 0.9.
   60% of 90 = 54
3. Compare. Sam is right if 60 is more than 54.
   60 > 54
4. Write the answer.
   Yes. 40% of 150 is 60, which is more than 54.

Check. 60 is more than 54, so Sam is right. ✓

Watch out. Find both amounts before you decide. Do not compare 40 with 60.

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. Find the Year 6 pupils first, then the choir.

1. Find the Year 6 pupils: 30% of 320. 10% is 32, so 30% is 3 lots of 32.
   3 × 32 = 96
2. Find the choir: 25% of 96. A quarter is 96 ÷ 4.
   96 ÷ 4 = 24
3. Write the answer.
   24

Check. 96 × 25% = 96 ÷ 4 = 24. ✓

Watch out. The 25% is of the Year 6 pupils, not of the whole school.

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. Find the price after each discount, then compare.

1. Shop A: find 20% of £45. 1% of £45 is £0.45, so 20% is 20 lots of that.
   20% of 45 = 9, so 45 - 9 = 36
2. Shop B: find 25% of £52. A quarter of 52 is 52 ÷ 4.
   25% of 52 = 13, so 52 - 13 = 39
3. Compare the prices. The lower price is the better buy.
   36 < 39
4. Write the answer.
   Shop A (£36 against £39).

Check. Shop A costs £36 and Shop B costs £39, so Shop A is cheaper. ✓

Watch out. Find the price to pay after the discount, not just the saving.