Using %s

(I) NON-CALCULATOR

Many % s can be found without a calculator if we remember the following simple connections.

(1) 50% = ½ .

(2) 25% = ¼.

(3) 10% = 1/10

(4) 1% = 1/100

Ex1 To find 15% of 160kg ………

10% of 160kg = 16kg

5% of 160kg = 8kg

So 15% of 160kg = 24kg

Ex2 To find 55% of £4200 ………

50% of £4200 = £2100

5% of £4200 = £210

So 55% of £4200 = £2310

Ex3 To find 371/2% of 160kg ………

25% of 160kg = 40kg

121/2% of 160kg = 20kg

So 371/2% of 160kg = 60kg

Ex4 To find 31/2% of £4200 ………

1% of £4200 = £42

3% of £4200 = £126

1/2% of £4200 = £21

So 31/2% of £4200 = £147

Exercise

(1) 171/2% of £64 …. 10% of £64 = £6.40

5% of £64 = £3.20

21/2% of £64 = £1.60

So 171/2% of £64 = £11.20

(2) 621/2% of £56.80 …. 50% of £56.80 = £28.40

25% of £56.80 = £14.20

121/2% of £56.80 = £7.10

So 621/2% of £56.80 = £35.50

Percentages & Decimals

USING A CALCULATOR

Simple Rule - Must be Learned

23% = 0.23, 77% = 0.77, 6% = 0.06,

NB: 60% = 0.60 or 0.6

Conversely

0.78 = 78%, 0.41 = 41%, 0.07 = 7%, 0.025 = 2.5%

Example

34% of £45.50 = 0.34 X £45.50 = £15.47

Example

A bank pays interest of 3.7% per annum (yearly).

Find the interest paid on £1290.

Interest = 3.7% of £1290 = 0.037 X £1290 = £47.73

% Reductions

Example

In a sale a TV set that normally costs £380 is reduced by 35%.

Find the sale price.

Long Method

Saving = 35% of £380 = 0.35 X £380 = £133

Sale price = £380 - £133 = £247

Short Method (by multiplier)

NB: removing 35% leaves 65% or 0.65

Sale price = 0.65 X £380 = £247

Timed Questions

Copy & complete the following

Ex1 Hi-fi - usual price £650 - Saving = 30%

% paid = 70%

Cost = 70% of £650 = 0.7 X £650 = £455

Ex2 Sofa - usual price £1200 - Saving 42%

% paid = 58%

Cost = 58% of £1200 = 0.58 X £1200 = £696

Exercise

Now try the following setting out the answers the same way.

(1) DVD Player: usual price = £280 Saving = 22%

(2) Bed: usual price = £475 Saving = 34%

(3) Wig: usual price £160 Saving 19%

% paid = 78%

Cost = 78% of £280 = 0.78 X £280 = £218.40

% paid = 66%

Cost = 66% of £475 = 0.66 X £475 = £313.50

% paid = 81%

Cost = 81% of £160 = 0.81 X £160 = £129.60

Exercise

Now try the following setting out the answers the same way.

(4) CD Player: usual price = £190 Saving = 32%

(5) Fridge: usual price = £470 Saving = 18%

(6) Cinema ticket: usual price £4.80 Saving 20%

% paid = 68%

Cost = 68% of £190 = 0.68 X £190 = £129.20

% paid = 82%

Cost = 82% of £470 = 0.82 X £470 = £385.40

% paid = 80%

Cost = 80% of £4.80 = 0.80 X £4.80 = £3.84

(7) Jeans: usual price = £37.50 Saving = 28%

(8) Calculator: usual price = £8.95 Saving = 31%

(9) Fish Supper: usual price £4.35 Saving 44%

% paid = 72%

Cost = 72% of £37.50 = 0.72 X £37.50 = £27

% paid = 69%

Cost = 69% of £8.95 = 0.69 X £8.95 = £6.18

% paid = 56%

Cost = 56% of £4.35 = 0.56 X £4.35 = £2.44

Important Point

Increasing a quantity by 12% gives us 112% of what we had already,

Increasing a quantity by 8% gives us 108% of what we had already,

and 112% = 1.12.

and 108% = 1.08.

This can now be used as follows …..

% Increasess

Example

A waitress earns £4.20 an hour but gets a 5% pay rise.

Find her new pay rate.

Long Method

Rise = 5% of £4.20 = 0.05 X £4.20 = £0.21

New rate = £4.20 + £0.21 = £4.41

Short Method (by multiplier)

NB: adding 5% gives 105% or 1.05

New rate = 1.05 X £4.20 = £4.41

Timed Questions

Copy & complete the following

Ex1 Joiner - usual rate £9.50 per hour - Increase = 12%

New % = 112%

New rate = 112% of £9.50 = 1.12 X £9.50 = £10.64

Ex2 Town population = 12000 - Increase 43%

New % = 143%

New population = 143% of 12000 = 1.43 X 12000

= 17160