\(\text{25}\%\) of \(\text{R}\,\text{124,16}\)
\(\text{25}\% = \frac{\text{1}}{\text{4}}\). \(\frac{\text{1}}{\text{4}} \text{ of } \text{R}\,\text{124,16} = \text{R}\,\text{124,16} \div \text{4} = \text{R}\,\text{31,04}\)
1.7 Percentages
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1.6 Ratio, rate and proportion
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End of chapter activity
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1.7 Percentages (EMGZ)
- Percentage
- A number represented as a part of \(\text{100}\).
How to calculate a percentage of an amount (EMG32)
- Write the percentage as a fraction with the denominator \(\text{100}\), 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.
Worked example 16: Working out percentages of amounts
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?
- \(\text{43}\% = \text{43} \div \text{100}\) \(\frac{\text{43}}{\text{100}} \times \text{50 586 757} = \text{21 752 305}\) people live in rural areas. With a calculator: To find \(\text{43}\%\) of \(\text{50 586 757}\) key in: \(\text{43} \div \text{100} \times \text{50 586 757} =\) OR \(\text{43}\% \times \text{50 586 757} =\)
- \(\text{80}\% = \text{80} \div \text{100}\) \(\frac{\text{80}}{\text{100}} \times \text{1 291} = \text{1 032}\) 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.
Worked example 17: Working out one amount as a percentage of another amount
Top Teenage T-shirts printed \(\text{120}\) T-shirts. They sold \(\text{72}\) T-shirts immediately. What percentage of the T-shirts were sold?
\(\text{72}\) of the \(\text{120}\) T-shirts were sold
\(\text{72} \div \text{120} \times \text{100} = \text{60}\%\). So \(\text{60}\%\) of the T-shirts were sold.
Calculating the percentages of amounts
Exercise 1.10
Calculate the following without a calculator:
\(\text{50}\%\) of \(\text{30}\) \(\text{mm}\)
\(\text{50}\% = \frac{\text{1}}{\text{2}}\). \(\frac{\text{1}}{\text{2}} \text{ of } \text{30}\text{ mm} = \text{30}\text{ mm} \div \text{2} = \text{15}\text{ mm}\)
Using your calculator and calculate:
\(\text{15}\%\) of \(\text{R}\,\text{3 500}\)
\(\text{R}\,\text{525}\)
\(\text{12}\%\) of \(\text{25}\) litres
\(\text{3}\) litres
\(\text{37,5}\%\) of \(\text{22}\) \(\text{kg}\)
\(\text{8,25}\) \(\text{kg}\)
\(\text{75}\%\) of \(\text{R}\,\text{16,92}\)
\(\text{R}\,\text{12,69}\)
\(\text{18}\%\) of \(\text{105}\) \(\text{m}\)
\(\text{18,9}\) \(\text{m}\)
\(\text{79}\%\) of \(\text{840}\) \(\text{km}\)
\(\text{663,6}\) \(\text{km}\)
Calculate what percentage the first amount is of the second amount (you may use your calculator):
\(\text{120}\) of \(\text{480}\)
\(\text{25}\%\)
\(\text{23}\) of \(\text{276}\)
\(\text{8,3}\%\)
\(\text{3 500}\) \(\text{ml}\) of \(\text{5}\) litres
\(\text{70}\%\)
\(\text{750}\) \(\text{g}\) of \(\text{2}\) \(\text{kg}\)
\(\text{37,5}\%\)
\(\text{4}\) out of \(\text{5}\) for a test
\(\text{90}\%\)
\(\text{2}\) out of \(\text{14}\) balls
\(\text{14,3}\%\)
Percentage discounts and increases (EMG33)
Look at the following extracts from newspaper articles and adverts:
- Cost price
- The amount that the dealer / trader / merchant pays for an article.
- Marked price
- This is the price of the article.
- Selling price
- This is the price after discount.
- Profit
- Sale price \(-\) cost price.
Discounts and increases
Exercise 1.11
The price of a tub of margarine is \(\text{R}\,\text{6,99}\). If the price rises by \(\text{10}\%\), how much will it cost?
New price is \(\text{R}\,\text{6,99}\) + \(\text{10}\%\) of \(\text{R}\,\text{6,99}\)= \(\text{R}\,\text{6,99}\) + \(\text{70}\) \(\text{c}\) (rounded off) = \(\text{R}\,\text{7,69}\) OR New price is (\(\text{100}\) + \(\text{10}\))\% of \(\text{R}\,\text{6,99}\) = \(\text{110}\%\) of \(\text{R}\,\text{6,99}=\frac{\text{110}}{\text{100}} \times \frac{\text{6,99}}{\text{1}}= \text{R}\,\text{7,69}\) (rounded off)
Top Teenage T-shirts have a \(\text{20}\%\) discount on all T-shirts. If one of their T-shirts originally cost \(\text{R}\,\text{189,90}\), what will you pay for it now?
You only pay \(\text{80}\%\) (\(\text{100}\%\) \(-\) \(\text{20}\%\) discount). Thus: \(\frac{\text{80}}{\text{100}} \times \text{189,901} = \text{R}\,\text{151,92}\) OR \(\text{20}\%\) of \(\text{R}\,\text{189,90} = \frac{\text{20}}{\text{100}} \times \text{189,901}\). The discount is thus \(\text{R}\,\text{37,98}\). You pay \(\text{R}\,\text{189,90} - \text{R}\,\text{37,98} = \text{R}\,\text{151,92}\).
Look at the pictures below. What is the value of each of the following items, in rands?
\(\text{R}\,\text{239,96} - \text{R}\,\text{59,75} = \text{R}\,\text{180,21}\)
\(\text{R}\,\text{299,50} - \text{R}\,\text{44,925} = \text{R}\,\text{1 254,58}\)
\(\text{R}\,\text{9 875} + \text{R}\,\text{790} = \text{R}\,\text{10 665}\)
\(\text{R}\,\text{15 995} + \text{R}\,\text{799,75}= \text{R}\,\text{16 794,75}\)
Calculate the percentage discount on each of these items:
\(\frac{\text{R}\,\text{1 360}}{\text{R}\,\text{1 523}} = \text{89}\%\). So discount is \(\text{100}\% - \text{89}\% = \text{11}\%\)
\(\frac{\text{R}\,\text{527,40}}{\text{R}\,\text{586}} = \text{90}\%\). So discount is \(\text{100}\% - \text{90}\% = \text{10}\%\)
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1.6 Ratio, rate and proportion
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