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Initial Ideas for percentage calculations

During the following ideas I will be suggesting a variety of methods for solving certain percentages problems. Those involving calculators are invariably quicker, however will fail on a non-calculator paper.

What does one percent or 1% actually mean?

Many students have a mental block when it comes to percentages because they are unable to understand whan one percent of an amount actually means
All you need to do to find noe percent of an amount is to DIVIDE BY 100
Percent means per hundred

Examples of finding simple percentages

a) To find 1% of £300, you do £300 ÷ 100 = £3

b) To find 2% of £300, one way is to find 1% first. We know this is £3. We then multiply by 2 to find 2%. 2 ×. £3 = £6

c) So, if we wanted to find 7% of £40. To find 1% we do £40 ÷100 = £0.40
Then, to find 7% we do 7 × £0.40= £2.80

Using a calculator to find percentages quickly


There are short-cuts you can use if a calculator is at hand. It is worth learning these.

a) To Find 15% of £300 you can do 0.15× £300 = £45

b) To find 27% of £40, do 0.27×£40 = £10.80

c) To find 7% of £30, do 0.07 × £30 = £2.10

Increasing and decreasing by percentages


a) Suppose we are told that a TV cost £300 and that this increased by 3%. What is the new cost

METHOD 1: 3% of £300 = £9. So new cost is £309

METHOD 2: 1.03 × £300 = £309.
The .03 corresponds to the 3% increase
The 1. to the fact that the TV is increasing

b) A person puts £100 into a savings account. This money increases by 5% each year. How much will he have after 3 years?

METHOD 1:
After year 1 he will have an extra 5% of £100 ie£105
After year 2 he will have an extra 5% of £105, ie £110.25
After year 3 he will have an extra 5% of £110.25 ie £115.76 (rounded to 2 d.p)

METHOD2:
1.05 × 1.05 × 1.05 × £100 = £115.76
Each multiple of 1.05 corresponds to each of the three years.

IMPORTANT: Note that this is not the same as finding 15% of £100. This would give £115.00 exactly

c) A car initially costs £9000, this decreases by 7&. Find the new cost.

METHOD 1: 1% of £9000 = £90. 7% = 7 × 90 = £630
New cost = £9000 - £630 = £8370

METHOD 2: 0.80 ×l £9000 = £8370
The .80 corresponds to a decrease of 20%, ie we are finding 80%
The 0. corresponds to the fact that the car has reduced in value

A quick way to do VAT or value added tax

Any goods which are classed as non-essential items have a tax of 17.5% added in England. This percentage varies from country to country
Suppose a car should cost £7000. To find the VAT:

METHOD1:
10% of £7000 = 700 (divided by 10)
5% of £7000 = 350 (divide 10% by 2)
2.5% of £7000 = £175 (divide 5% by 2)
Add these together to get VAT = 700 + 350 + 175 = £1225

METHOD1 (Using a calculator) 0.175 × £7000 = £1225