3.8 How to calculate a percentage of an amount

Mathematics

Percentages

Educator section

Memorandum

• (i) 23 909 920

1. 42 840 000
2. 320

15.3.1

a) R31,04

b) 15 mm

15.3.2

a) R525

b) R3,00

c) 8,25 kg

d) R12,69

16.3

a) 25%

b) 8, $\stackrel{\text{.}}{3}$ %

c) 70%

d) 37,5%

e) 80%

f) 66, $\stackrel{\text{.}}{6}$ %

Leaner section

Content

Acticity: how to calculate a percentage of an amount [lo 1.7.6, lo 1.9.2, lo 2.7.1 ]

a) Work together with a friend. Can you calculate the answers with the help of a calculator?

(i) How many people live in rural areas?

(ii) How many votes did the ANC get?

(iii) How many patients were heavy smokers?

b) How did you calculate the answers?

15.2.1 REMEMBER!

To calculate the percentage of an amount:

a) Write the percentage as a fraction with the denominator 100 ORWrite the percentage as a decimal fraction

b) Multiply this fraction / decimal fraction with the amount / number / quantity that is given

In the example above:

$\begin{array}{}\frac{\text{58}}{\text{100}}\times \frac{\text{41}\text{224}\text{000}}{1}\\ \frac{\text{58}\text{41}\text{224}\text{000}}{\text{100}}\\ =\text{23}\text{909}\text{920}\text{people}\end{array}$ OR 

15.2.2 Remember also!

With a calculator: multiply 41 224 000 by 58 %

You will thus key in: 58 ÷ 100 × 41 224 000 =

OR

58% × 41 224 000 =

15.3.1 Calculate the following without a calculator:

1. 25% of R124, 16

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b) 50% of 30 mm

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15.3.2 Use your calculator and calculate:

1. 15% of R3 500

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b) 12% of 25

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c) 37,5% of 22 kg

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d) 75% of R16,92

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16. One amount as a percentage (%) of another amount

16.1 Work together with a friend. Look carefully at the following problem and the solution.

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

72 % of the 120 T-shirts were sold : thus $\frac{\text{72}}{\text{120}}$ % means something out of 100

Thus: $\frac{\text{72}}{\text{120}}\times \frac{\text{100}}{1}$ =60%

16.2 REMEMBER!

To calculate % of amounts:

a) Convert first to the same unit

b) Express the given amounts as a fraction :

c) Multiply it by 100

16.3 Calculate how much % the first amount is of the second amount (you may use your calculator):

a) 120 of 480

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b) 23 of 276

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c) 3 500 ml of 5 litre

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d) 750 g of 2 kg

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e) 4 out of 5 for a test

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f) 2 out of balle

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Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.7.6 finding percentages;

Assessment Standard 1.9: We know this when the learner uses a range of techniques to perform calculations including:

1.9.2 using a calculator.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.7: We know this when the learner determines, analyses and interprets the equivalence of different descriptions of the same relationship or rule presented:

2.7.1 verbally.