Getting sick of powerpoints yet?

Now it is time for calculators

If you haven’t got one it may get difficult

Writing a fraction as a percentage

We saw that 7 = 35 = 35%

20 100

With more difficult fractions this is not so simple eg. 23

35

23 as a percentage 35

Write the fraction as a decimal

23 = 23 ÷ 35 = 0.657142857…..

35

Multiply by 100

0.657142857 x 100 = 65.7% (to 1 d.p.)

18 as a percentage 70 18 = 18 ÷ 70 = 0.2571…….

70

0.2571 x 100 = 25.7% (to 1 d.p.)

Now for finding a percentage of an amount

Two slightly different approaches

Method 1

1. Find 1% by dividing by 100

2. Multiply this by the percentage you want to find

Find 32% of 450• 1% of 450 = 4.5

(450÷100)• 32% of 450 =

32 x 4.5 = 144

Try this one – 27% of 46

• 1% of 46 = 46 ÷ 100

= 0.46

• 27% of 46 = 27 x 0.46

= 12.42

Method 2

1. Change the percentage you want to find into a decimal

2. Multiply your ‘amount’ and ‘decimal percentage’ together

Find 62% of 93• 62% = 0.62• 62% of 93 = 0.62 x 93

= 57.66

Try this one – 87% of 58

87% = 0.87

87% of 58 = 0.87 x 58

= 50.46

The second method is important for questions involving

‘compound interest’

Compound interest is paid at regular intervals (usually

yearly)…

You earn interest on your total amount (original amount plus any interest you

have already received)

Need to write the percentage as a decimal

• If you are paid 8% interest, you will end up with 108% of your starting amount.

• 108% as a decimal is 1.08

• Instead of finding 8% and adding it on, you can find 108% by multiplying by 1.08

The value of a £52000 house goes up 4% - find the new value

• House is now worth 104% of what it was originally

• 104% = 1.04 (104 ÷ 100)

• New value = £52000 x 1.04

= £54080

A teacher gets a 2.5% pay rise. If he was paid £18500 originally,

what is his new salary?• Salary is now 102.5% of what it started at

• 102.5% = 1.025 (102.5 ÷ 100)

• New salary = £18500 x 1.025

= £18962.50

We can use these ‘multipliers’ when a value decreases too.

The value of a car falls 14% from its value of £9800. Find the new

value

• Car is now worth 86% (100 – 14) of its original value.

• 86% = 0.86 (86 ÷ 100)

• New value = £9800 x 0.86

= £8428

Find the multipliers which correspond to these percentage

increases/decreases

8% decrease 0.92

7% increase 1.07

14% increase 1.14

36% decrease 0.64

17.5% increase 1.175

3.5% decrease 0.965

Compound interest for yearly savings

n = number of years

Savings = original savings x (percentage)

percentage must be written as multiplier

eg. 6% interest = 1.06

n

If you put £500 in a bank for 4 years and were paid 3% interest per year –how much

would you have? Savings = original savings x (percentage)

Percentage = 3% so multiplier = 1.03

No. of years, n = 4

Savings = £500 x 1.03

= £562.75

n

4

If you put £100 in a bank for 24 years and were paid 4% interest per year –how much

would you have? Savings = original savings x (percentage)

Percentage = 4% so multiplier = 1.04

No. of years, n = 24

Savings = £100 x 1.04

= £256.33

n

24

Also works for decreases

A car loses 12% of its value each year. What is it worth after 7 years if

it cost £12000 when new?

12% decrease = 0.88

Value = £12000 x 0.88

= £4904.11

7

Percentage Increase

And decrease

Really easy..

% increase (decrease) =

increase (decrease) x 100%

original value

A house was bought for £46000 and is now worth £82000. Find the percentage increase in the value

of the house.

Increase = 82000 – 46000 = £36000

Percentage = 36000 x 100%

increase 46000

= 78.2%