## Percentages

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

**How to calculate a percentage of an amount**

- 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 \(\text{20}\% = \text{0,2}\). - 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:

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

**Answer**

- \(\text{43}\% = \text{43} \div \text{100}\)

\(\frac{\text{43}}{\text{100}} \times \text{50 586 757} = \text{21 752 305}\) 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

\(\text{43}\% \times \text{50 586 757} =\) - \(\text{80}\% = \text{80} \div \text{100}\)

\(\frac{\text{80}}{\text{100}} \times \text{1291} = \text{1032}\) patients - \(\text{73}\% = \text{73} \div \text{100}\)

\(\frac{\text{73}}{\text{100}} \times \text{21 700 000} = \text{15 841 000}\) 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?

**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:

25% of R 124,16

50% of 30 mm

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

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

Using your calculator and calculate:

15% of R 3500

12% of 25 litres

37,5% of 22 kg

75% of R 16,92

18% of 105 m

79% of 840 km

R 525

3 litres

8,25 kg

R 12,69

18,9 m

663,6 km

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

120 of 480

23 of 276

3500 ml of 5 litres

750 g of 2 kg

4 out of 5 for a test

2 out of 14 balls

25%

8,3%

70%

37,5%

90%

14,3%

**Percentage discounts and increases**

Look at the following extracts from newspaper articles and adverts:

- 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?

\(\text{R 239,96} - \text{R 59,75} = \text{R 180,21}\)

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

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

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

Calculate the percentage discount on each of these items:

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

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