Percentages

Percentages

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Finding a percentage of a number

Find 85% of £65

non-calculator method

  • 80% = 10% multiplied by 8 = 52
  • 5% = 10% divided by 2 = 3.25

so 52+3.25=55.25

calculator method

65 divided by 0.85 = 55.25

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Increasing amounts

A shop has an increase in a new products price, they increase a £40 toy car by 20%, what is the new price

Non-calculator method

  • 10% = 40 divided by 10 = 4
  • 20% = 10% multiplied by 2 = 8

so, 40+8 = £48

Calculator method

40 multiplied by 1.2 = £48 

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The percentage one number is of another

To workout what one number is of another:

1) write the number as a fraction.

2) Change the fraction to a decimal.

3) Change the decimal to a percentage.

Example

What percentage is £15 of £80?

15/80 = 15 divided by 80 = 0.1875 = 18.75%

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Real life examples

Example 1

3/5 of a class ate pizza for lunch, in a percentage how many people is that?

3/5 = 3 divided by 5 = 0.6

0.6 = 60%

Example 2

In a fraction, how much pizza is eaten if 80% has gone mysteriously?

80% = 80/100 = 4/5

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Compound interest

If you earn 2% compound interest each year then the amount increases a little bit each time because after the frirst year you would take 2% of the whole amount ( including last years interest).

An easy way to solve this is:

£125 in the bank increases by 6% compound interest for 5 years.

125 multiplied by 1.06 ^5

1.06 is the percentage increase and the number acting as the indices is the number of years.

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Simple interest

Example

Sally deposits £600 into an account with an interest rate of 5% per annum.

Calculate the interest that Sally receives in one year and find how much money she has in the account after one year.

Interest = 5% of £600

5/100 multiplied by £600 = £30

After one year sally would have saved £600+£30=£630

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Decreasing amounts

A toy car was £40 was reduced by 20% in a sale, what is the new price?

  • £40 multiplied by 0.2 = 8
  • Take this number away from the original value
  • £40 - £8 = £22
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Reverse percentages

A house increases in value by 20% to £72,000. Find out what it was worth before the increase.

£72,000 = 120%

Divide by 120: £600 = 1%

£600 multiplied by 100 = £60,000 = 100%

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Percentage change

Example

You had 5 books, but now have 7. The change is: 7-5 = 2.

So the percentage change from 5 to 7 is: 2/5 = 0.4 = 40%

Step 1: Calculate the change (subtract old value from the new value) Step 2: Divide that change by the old value (you will get a decimal number) Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

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