Year 6 Percentages: check-up and SATs-style questions

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.