Part 4: Percentages

from Grade 11 Study Guide Mathematics Literacy

Part 4: Percentages

A percentage is a way of expressing the parts of a whole (the numerator) as a value out of 100. It is always written with the % symbol directly after the number. A percentage can also be written as a fraction. The denominator will always be 100. The term ‘per cent’ derives from the Latin word per centum, which means ‘per hundred’ or ‘for every hundred’.

Percentages can be expressed as a common fraction or as a decimal number, e.g. 83% = 83

100 OR = 0,83.

4.1 Calculation of percentage

To calculate a percentage of an amount, write the per cent as a fraction and multiply by the amount.

percent 100 ×amount

EXAMPLES

4.1.1 Calculate 25% of R5 000,00.

Note: The word ‘of’ means multiplication.

25 100 × R5 000 = R1 250,00

Sequence on calculator: (25 ÷ 100) × 5 000 =

4.1.2 Thandi gets 28

in a Mathematical Literacy test. What is her percentage for the test?

28 40 × 100 = 70%

Sequence on calculator: (28 ÷ 40) × 100 =

4.2 Determining new values for given percentages

Sometimes we need to calculate the new price of an item or product after it has been increased by a certain percentage, e.g. VAT (Value added tax) which is levied on the original price.

EXAMPLES

4.2.1 A packet of biscuits costs R15,30 without VAT. How much will you pay after VAT is added?

(In South Africa, the VAT rate is currently 15%)

15 100 × R16,00 = R2,40 OR R16,00 × 115% = R18,40

R16,00 + R2,40 = R18,40

You will pay R18,40 after VAT is added.

4.2.2 A vendor increases his prices by 8%. If the original price is R45,99, what will the price be after the increase?

8 100 × R45,99 = R3,68 OR R45,99 × 108% = R49,67

R45,99 + R3,68 = R49,67

The new price is R49,67.

4.2.3 A shoe shop has a sale with 25% off all shoes. What will you pay for a pair of shoes that was originally priced at R645,00?

25 100

× R645,00 = R163,50 OR 100% – 25% = 75% R645,00 – R163,50 = R490,50 75% × R645,00 = R490,50

4.2.4 The petrol price decreases with 2,5%. How much will motorists now pay for a litre of petrol if the price was R14,40/ℓ?

2,5 100

× R14,40 = R0,36 OR 100% – 2,5% = 97,5% R14,40 – R0,36 = R14,04 97,5% × R14,40 = R14,04

Motorists will now pay R14,04/ℓ.

4.3 Determining the initial value when new values and percentages are given

Sometimes we need to calculate the original price of an item or product before it has been decreased by a certain percentage, e.g. discount on products during a sale.

Important

You must determine the original value – the previous value, before it was increased or decreased.

EXAMPLES

4.3.1 Dishwashing liquid costs R23,10, VAT included. VAT is 15%. What was the dishwashing liquid’s price before VAT was added?

P: price without VAT P × 115% = R23,10 P =

23,10 115% P = R20,09 (115% = 100% + 15%) OR R23,10 ÷ 1,15

The dishwashing liquid’s original price was R20,09.

4.3.2 A butchery increases their prices by 9%, which means that biltong now costs R195,10/kg. What was the original price before the increase?

P: original price P × 109% = R195,10 P = 195,10 ÷ 109% = R178,99

The biltong’s original price was R178,99.

4.3.3 A computer shop has a sale with all items at 25% discount. If a printer’s selling price is currently at R1 538,40, what was the original price before the discount?

P: original price (100% – 25% = 75%)

P × 75% = R1 538,40 P = R1 538,40 ÷ 75% = R2 051,20

The printer’s original price was R2 051,20.

4.4 Percentage increase and decrease

We can use the following formula to determine percentage increase or decrease:

Percentage increase/decrease = currentvalue−previousvalue previousvalue ×100

EXAMPLES

4.4.1 In 2019, a school had 1 538 learners and in 2020, there were 1 645 learners. By what percentage has the enrolment increased?

Percentage increase = ��−��

= 6,96% ≈ 7%

4.4.2 In 2018, a glass factory produced 796 faulty glasses and in 2019, only 675. By what percentage did the faulty glasses decrease?

Percentage decrease =

= -15,20%

The negative value indicates a decrease. In this example, the percentage of faulty glasses decreased by 15,20%.