Functional Skills Mathematics Level 2

Learning Resource 7 Percentages

N2/L2.2

N2/L2.7

N2/L2.8

N2/L2.9

PERCENTAGES LEVEL 2 Excellence in skills development

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Contents Order and Compare Percentages

N2/L2.7

Pages 3 - 5

Understand Percentage Increase and Decrease

N2/L2.7

Pages 6 - 7

Finding Percentage Parts

N2/L2.8

Pages 8 - 10

Evaluating as a Percentage

N2/L2.9

Pages 11 - 12

Fraction/Decimal Fraction/ Percentage Equivalencies

N2/L2.2

Pages 13 - 14

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Information

7

Order and Compare Percentages

To order or compare percentages is quite straightforward; you simply put them in number order, e.g. 5% 10% 14% 23% 54%. Sometimes you are asked to order or compare the actual calculated percentage quantities. In this case you need to work out each quantity and then compare. There are some percentages that can be worked out easily: 25% =

1 4

To find 25% of a number you divide it by 4.

50% =

1 2

To find 50% of a number you divide it by 2.

75% =

3 4

To find 75% of a number: find 50% and 25% and then add them together.

10% =

1 10

To find 10% of a number you divide by 10.

If you can find 10%, then lots of other percentages are easy: 5%

First find 10%, then half it.

20%

Find 10%, then double it (times by 2).

30%

Find 10%, then times by 3.

40% etc.

Find 10%, then times by 4.

What about 15%? 15%

Find 10% and 5% of the number and then add them together.

To find 65%? 65%

Find 60% and 5% of the number and then add them together.

Once you have found the calculated quantities, you can then put them in order or compare them as required.

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Example 1

7

Order and Compare Percentages

Put the following in order from smallest to largest: 25% of 160

20% of 180

30% of 130

To find 25% of 160, divide by 4:

160 4

To find 20% of 180, first find 10% then times by 2:

180 10

To find 30% of 130, first find 10% then times by 3:

130 10

=

40

x2

=

36

x3

=

39

The order from smallest to largest is 20% of 180

30% of 130

25% of 160

Neither the percentages nor the numbers are in order. It is the actual calculated quantity or amount that is put in order. Example 2 Which is the largest amount? 40% of £75

75% of £40

35% of £90

To find 40% of £75, first find 10% then times by 4:

75 10

x4

=

£30

=

£30

=

£31.50

To find 75% of £40, find 50% and 25% and add them together: 40 2

= 20

40 4

= 10

20 + 10

To find 35% of £90, find 30% and 5% and add them together: 90 10

x3

= 27

90 10

x

1 2

=4

1 2

27 + 4

1 2

35% of £90 is the largest amount.

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Exercise 1 1)

7

Order and Compare Percentages

Lucy wants to insure her car and has had quotes from three separate insurers; ‘One’ Insurance ‘Best’ Insurance ‘Deal’ Insurance

£295 with a 20% discount £285 with a 15% discount £318 with a discount of 25%.

Order the quotes after discount, starting with the lowest. Lowest £ 2)

£

£

Leon earns £20,500 and gets a 5% pay-rise. Kimberley earns £22,500 and gets a 4.5% pay rise. Who gets the bigger cash increase in their annual salary? Leon / Kimberley

3)

4)

Which of these statements are true? a)

50%

of

£28

b)

75%

of

£28

c)

65%

of

£40

d)

15%

of

£150

e)

35%

of

£115

< = > = >

True / False 40%

of

£12

25%

of

£95

15%

of

£120

25%

of

£90

60%

of

£80

The following discounts are being offered on microwaves at the local electrical superstore.

After deductions, what is the price of the cheapest microwave?

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Information

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Understand Percentage Increase and Decrease

If an amount has increased by a percentage: calculate the percentage amount then add it to the original figure to find the new amount. Or you can add the percentage increase to the original percentage (100%) and then do the calculation. If an amount has decreased by a percentage: calculate the percentage amount then subtract it from the original figure to find the new amount. Or you can subtract the percentage decrease from the original percentage (100%) and then do the calculation. Examples Your meal costs £56 but there will be a 10% service charge added. How much will you pay in total? Original price = £56

Increase = 10% 56 10

To find 10% of £56 , divide by 10. Add increase to original price

£56 + £5.60

=

£5.60

=

£61.60

You will pay £61.60 Another way of calculating this is to add the percentages together first. Original price (100%) + 10% £56 x 110%

= 110%

110 = 56 x 100

= 61.6

= £61.60

House prices decreased by 5% between 2007 and 2008. If a house was valued at £150,000 in 2007, what would it be worth in 2008? Original price = £150,000

Decrease = 5% 150000 1 x 10 2

=

£7500

£150,000 - £7500

=

£142,500

To find 5% of £150,000 , first find 10% then half it. Subtract decrease from original price The house would be worth £142,500 in 2008.

Another way of calculating this is to subtract the decrease percentage first. Original price (100%) - 5% £150,000 x 95%

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95 = 150000 x 100

= 95% = 142,500

= £142,500

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Exercise 2 1)

7

Understand Percentage Increase and Decrease

End of line sports equipment has been reduced by 30%. What will the sale prices be after taking off the 30% discount? a) £98.50

b)

£72

c) £185

d) £38.50

2)

My electricity bill is £76.50 before VAT is added at a special rate of 8%. How much is my bill including VAT?

3)

The coffee shop has to increase some of their prices by 20%. Work out the new prices. Item Fruit scone with cream Danish pastry Warm waffles with cherries Chocolate muffin Carrot cake Cheesecake with cream

Original Price £1.95 £1.75 £2.50 £1.05 £1.85 £2.20

Price Increase

New Price

4)

A new house is being built. The cost has increased by 15% from the original £96,000. What does it cost now?

5)

A rail season ticket of £540 rises by 12%. What will it now cost?

6)

Tony has increased his lawn by 6%. If the lawn area was 46.67m2 , how big is it now? (Round to two decimal places.)

7)

There are 40 chocolates in a box. Hannah ate 25%, Melissa ate 30%, how many chocolates were left for Shannon?

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Information

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Finding Percentage Parts

Some percentages are easy to find without a calculator: 50% is the same as a half – so just divide by 2. 25% is the same as a quarter – so divide by 4 (or divide by 2 and then divide by 2 again). 10% is the same as a tenth – so divide by 10. You can find 5% by halving 10%, 20% by doubling 10% and so on. Sometimes, however, the percentage can be more complicated. VAT (Value Added Tax) is a tax set by government and is 17 1 % at the moment. The government can change 2

VAT at any time. You can work out 17 1 % by finding 10%, 5% and 2 1 % and adding them together. To find 2

2

10%, divide by 10; 5% is half of 10%;

21 2

% is half of 5%.

Example Work out the VAT on £700. VAT is 17 1 % 2

To find 17 1 % of £700, find 10%, 5% and 2 1 % and then add them together: 2

2

Find 10%

5% is half of 10%

2 1 % is half of 5%

700 10

70 2

35 2

= 70

70 + 35 + 17

1 2

=

122

= 35

2

= 17

1 2

1 2

The VAT on £700 is £122.50.

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Finding Percentage Parts

Percent means per hundred (out of every hundred). 25 ). 100 84 84% means 84 per hundred or 84 out of every hundred ( ). 100

25% means 25 per hundred or 25 out of every hundred (

To calculate the amount or quantity this represents, you multiply by the percentage and divide by 100. Examples Find 4% of 200 200 x

4 100

=

800 100

=

8

This is easy to check as you know that 4% of 100 is 4, so 4% of 200 should be 8. Find 25% of 200 200 x

25 100

=

5000 100

=

50

Again, it is easy to check that this works as 25% =

1 4

and 50 is

1 4

of 200.

Find 44% of 300 300 x

44 100

=

13200 = 100

132

Check: 44% of 100 is 44, so 44% of 300 is 44 x 3, which is 132. Find 27% of 176 176 x

27 100

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=

4752 100

=

47.52

9

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Exercise 3

7

Finding Percentage Parts

1)

A customer pays a 15% deposit on a new bike costing £120. How much is left to pay?

2)

What is 12 % of a population of 200,000?

3)

Jacob has won £850,000 on the lottery and decides to donate 30% to charity. How much will he be left with?

4)

These figures do not include VAT. Work out the VAT at 17 % on these prices:

1 2

1 2

a) £120

b) £434

c)

£688

d) £84.40

e) £756.40

f)

£5500

5)

Josie was disappointed when only 70% of 480 delegates attended the conference. How many people didn’t attend?

6)

Archie’s deductions from his pay are about 30%. If his pay is £215, how much will his deductions be?

7)

The badminton club has 280 members. If 65% are men, what is the total number of women?

8)

Sunny Days Travel are giving a 15% discount on all holidays booked before the end of the month.

Sunny Days Travel Destination Rimini Salou Alcudia Skiathos Alicante

Price per person £388 £637 £525 £695 £739

a)

What is the new price of a holiday to Alcudia?

b)

How much will it be for 2 people to go to Rimini with the discount taken off?

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Information

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Evaluating as a Percentage

Sometimes questions are asked the other way round. For example a question such as: What is 25% of 200? (Answer = 50) Can become What percentage is 50 of 200? You can solve this by writing it as a fraction and then multiplying by 100. So

50 1 = 200 4 1 100 × 100 = = 25% 4 4

Example There are 12 girls in a class of 20. What percentage of the class are girls? Write the figures as a fraction

12 20

(Note that the ‘’whole’’ is always on the bottom of the fraction.) 12 1200 × 100 = = 60% 20 20

60% of the class are girls.

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Exercise 4

PERCENTAGES LEVEL 2 N2/L2.9

Evaluating as a Percentage

1)

There are 80 cars in the car park. 24 of these cars belong to teachers. What percentage of the cars belong to teachers?

2)

A packet of washing powder usually costs £2.50. It has been reduced by 50p. What is the percentage reduction?

3)

In a tube of 48 smarties, 12 were coloured yellow. a)

What percentage were coloured yellow?

b)

There were 6 red smarties. What percentage of smarties were coloured red?

4)

Tony buys 25 bottles of wine. If 13 were red and 4 were rosé, what percentage were white?

5)

In the Art class there are 40 students, 16 are men. What % are women?

6)

a)

What is 170 g as a % of 200 g

b)

What % of £16 is 40p?

c)

What is 360 m as a % of 8000 m?

d)

What % of £65 is £3.90?

7)

7

Three hundred trains left the city station yesterday. Of these, 60 left late. What percentage of the trains left on time?

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PERCENTAGES LEVEL 2 N2/L2.2

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Information

7

Fraction/Decimal Fraction/Percentage Equivalencies

Percent means per hundred. Percentage = 75% 75% means 75 per hundred or Fraction =

75 . 100

75 3 which can be simplified to 100 4

Decimal Fraction

= 75 ÷ 100 = 0.75

Therefore 75%

=

3 4

= 0.75

Examples 75%

=

75 100

=

3 4

=

0.75

50%

=

50 100

=

1 2

=

0.5

25%

=

25 100

=

1 4

=

0.25

33%

=

33 100

=

1 (approx) = 3

0.33

67%

=

67 100

=

2 (approx) = 3

0.67

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Exercise 5 1)

7

Fraction/Decimal Fraction/Percentage Equivalents

Jill asked 4 friends to guess how many sweets were in the jar. Their estimates were: a)

2 3

b)

65%

c)

3 4

d)

0.78

21 50

d)

5 8

Which is the smallest of these estimates? 2)

Write these fractions as decimals. a)

3 20

______ 3)

2 5

b)

c)

______

______

______

Seventy people have been invited to a New Years Eve party. 1 were already going to a party and a further 20% didn’t want 10

to attend. How many are going to attend the party? 4)

5)

Put the following in order from lowest to highest. a)

40%

2 3

0.5

b)

0.65

75%

5 8

James got these scores in his exams. 45 50

12 30

48 60

English

Music

Art

Citizenship

a)

Convert these marks to %.

b)

Which subject did James get the highest and lowest score in? Highest _______________

6)

25 40

68 80

Maths

Lowest _______________

Put the following in order from highest to lowest. a)

0.4

70%

1 20

b)

30%

3 5

0.29

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