Menu

Percentages

Definition 1: Percentage
A number represented as a part of 100.

How to calculate a percentage of an amount

  1. Write the percentage as a fraction with the denominator 100, for example \(\text{20}\% = \frac{\text{20}}{\text{100}}\).
    OR write the percentage as a decimal fraction, for example \(\text{20}\% = \text{0,2}\).
  2. Multiply this fraction / decimal fraction with the amount that is given.

Let's see how this works in an example.

Example 1: Working out percentages of amounts

Question

Use a calculator to answer the following questions:

  1. Image
    How many people live in rural areas?
  2. Image
    How many T.B. patients are H.I.V. positive?
  3. Image
    How many people had never voted before the 1994 election?

Answer

  1. \(\text{43}\% = \text{43} \div \text{100}\)
    \(\frac{\text{43}}{\text{100}} \times \text{50 586 757} = \text{21 752 305}\) people live in rural areas.
    With a calculator:
    To find 43% of 50 586 757 key in:
    \(\text{43} \div \text{100} \times \text{50 586 757} =\)
    OR
    \(\text{43}\% \times \text{50 586 757} =\)
  2. \(\text{80}\% = \text{80} \div \text{100}\)
    \(\frac{\text{80}}{\text{100}} \times \text{1291} = \text{1032}\) patients
  3. \(\text{73}\% = \text{73} \div \text{100}\)
    \(\frac{\text{73}}{\text{100}} \times \text{21 700 000} = \text{15 841 000}\) people had never voted before.

Example 2: Working out one amount as a percentage of another amount

Question

Top Teenage T-shirts printed 120 T-shirts. They sold 72 T-shirts immediately. What percentage of the T-shirts were sold?

Image

Answer

72 of the 120 T-shirts were sold

\(\text{72} \div \text{120} \times \text{100} = \text{60}\%\). So 60% of the T-shirts were sold.

Exercise 1: Calculating the percentages of amounts

Calculate the following without a calculator:

  1. 25% of R 124,16

  2. 50% of 30 mm

  1. \(\text{25}\% = \frac{\text{1}}{\text{4}}\). \(\frac{\text{1}}{\text{4}} \text{ of } \text{R 124,16} = \text{R 124,16} \div \text{4} = \text{R 31,04}\)

  2. \(\text{50}\% = \frac{\text{1}}{\text{2}}\). \(\frac{\text{1}}{\text{2}} \text{ of } \text{30}\text{ mm} = \text{30}\text{ mm} \div \text{2} = \text{15}\text{ mm}\)

Using your calculator and calculate:

  1. 15% of R 3500

  2. 12% of 25 litres

  3. 37,5% of 22 kg

  4. 75% of R 16,92

  5. 18% of 105 m

  6. 79% of 840 km

  1. R 525

  2. 3 litres

  3. 8,25 kg

  4. R 12,69

  5. 18,9 m

  6. 663,6 km

Calculate what percentage the first amount is of the second amount (you may use your calculator):

  1. 120 of 480

  2. 23 of 276

  3. 3500 ml of 5 litres

  4. 750 g of 2 kg

  5. 4 out of 5 for a test

  6. 2 out of 14 balls

  1. 25%

  2. 8,3%

  3. 70%

  4. 37,5%

  5. 90%

  6. 14,3%

Percentage discounts and increases

Look at the following extracts from newspaper articles and adverts:

Image
Definition 2: Cost price
The amount that the dealer / trader / merchant pays for an article.
Definition 3: Marked price
This is the price of the article.
Definition 4: Selling price
This is the price after discount.
Definition 5: Profit
Sale price \(-\) cost price.

Exercise 2: Discounts and increases

The price of a tub of margarine is R 6,99. If the price rises by 10%, how much will it cost?

New price is R 6,99 + 10% of R 6,99= R 6,99 + 70 c (rounded off) = R 7,69 OR New price is (100 + 10)\% of R 6,99 = 110% of \(\text{R 6,99}=\frac{\text{110}}{\text{100}} \times \frac{\text{6,99}}{\text{1}}= \text{R 7,69}\) (rounded off)

Top Teenage T-shirts have a 20% discount on all T-shirts. If one of their T-shirts originally cost R 189,90, what will you pay for it now?

You only pay 80% (100% \(-\) 20% discount). Thus: \(\frac{\text{80}}{\text{100}} \times \text{189,901} = \text{R 151,92}\) OR 20% of \(\text{R 189,90} = \frac{\text{20}}{\text{100}} \times \text{189,901}\). The discount is thus R 37,98. You pay \(\text{R 189,90} - \text{R 37,98} = \text{R 151,92}\).

Look at the pictures below. What is the value of each of the following items, in rands?

  1. Image
  2. Image
  3. Image
  4. Image
  1. \(\text{R 239,96} - \text{R 59,75} = \text{R 180,21}\)

  2. \(\text{R 299,50} - \text{R 44,925} = \text{R 1254,58}\)

  3. \(\text{R 9875} + \text{R 790} = \text{R 10 665}\)

  4. \(\text{R 15 995} + \text{R 799,75}= \text{R 16 794,75}\)

Calculate the percentage discount on each of these items:

  1. Image
  2. Image
  1. \(\frac{\text{R 1360}}{\text{R 1523}} = \text{89}\%\). So discount is \(\text{100}\% - \text{89}\% = \text{11}\%\)

  2. \(\frac{\text{R 527,40}}{\text{R 586}} = \text{90}\%\). So discount is \(\text{100}\% - \text{90}\% = \text{10}\%\)