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Primary Maths · Year 6Chapter 6 · Percentages
Year 6 · Percentages · Lesson 6.3

Year 6: Building blocks: 10%, 1%, 50%, 25% and 75%

Part of the Year 6 percentages chapter. Chapter overview · whole chapter on one page

6.3

Building blocks: 10%, 1%, 50%, 25% and 75%

Year 6
Solve problems involving the calculation of percentages (of measures, such as 15% of 360)

Some percentages are easy to find in your head. They are the building blocks for harder ones like 15% or 35%.

Once you know 10% and 1%, you can build many other percentages from them. For example, 5% is half of 10%.

10 out of 100 = 10%
Ten squares are 10% of the grid. Dividing the whole by 10 gives 10%.

Key ideas

  • 10% of a number: divide by 10.
  • 1% of a number: divide by 100.
  • 50% = half, 25% = a quarter, 75% = three quarters.
  • Use the building blocks to find other percentages: 20% is 2 × 10%, and 5% is half of 10%.
Worked example 6.3.1
Find 10% of 260.

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.
    260 ÷ 10 = 26
  3. Write the answer. The answer is smaller than the amount.
    26

Check. 26 × 10 = 260. ✓

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

Worked example 6.3.2
Find 1% of 360.

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 360. Divide by 100, because 1% is one hundredth.
    360 ÷ 100 = 3.6
  3. Write the answer.
    3.6

Check. 3.6 is less than 360, because 1% is less than 100%. ✓

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

Worked example 6.3.3
Find 75% of 200.

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%.
    200 ÷ 4 = 50
  3. Multiply by 3. Three quarters is three lots of one quarter.
    50 × 3 = 150
  4. Write the answer.
    150

Check. 150 is less than 200, because 75% is less than 100%. ✓

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

Watch out

1% of 360 is 3.6, not 36. Dividing by 100 makes the number 100 times smaller, so the answer is a decimal.

Exam tip

Grown-up tip. Practise the building blocks aloud: “10% of 80 is 8, so 20% is 16.” Quick recall helps with the next section.

Exercise 6C  Percentages of amounts: the building blocks

Non-calculator
1
FFind 10% of each amount.
(a)10% of 50 =
(b)10% of 230 =
(c)10% of 780 =
(d)10% of 40 =
2
FFind 1% of each amount.
(a)1% of 500 =
(b)1% of 80 =
(c)1% of 2400 =
(d)1% of 7 =
3
FFind 50% of each amount.
(a)50% of 64 =
(b)50% of 37 =
(c)50% of 9 =
4
FFind 25% of each amount.
(a)25% of 60 =
(b)25% of 90 =
(c)25% of 36 =
5
FFind 75% of each amount.
(a)75% of 200 =
(b)75% of 40 =
(c)75% of 12 =
6
FQuick-fire! Work out each percentage.
(a)10% of 90 =
(b)1% of 450 =
(c)50% of 90 =
(d)25% of 36 =
(e)75% of 16 =
(f)10% of 4.5 =
7
PSA bag holds 250 g of sweets. Sam eats 10% of the sweets. How many grams (g) does he eat?
8
PSA school raises £640. 25% of the money goes to charity. How much (£) goes to charity?
9
PSA pizza costs £12. Mia gets 50% off the price, so she pays half. How much (£) does she pay?
10
PSJack has 80 stickers. He gives away 25% of them. How many stickers does he have left?
11
PSA town has 3600 homes. 1% of the homes have solar panels. How many homes have solar panels?
12
PSA sports club has 120 members. 75% of them are under 12. How many members are under 12?
13
RSam says that 10% of 500 is the same as 1% of 5000. Is he right? Explain your answer.
14
RElla says that 50% of 60 is the same as 25% of 120. Is she right? Explain your answer.

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