PERCENTAGES 2

Expressing one quantity as a percentage of a second quantity

To write one quantity as a percentage of a second quantity:1. Write the first quantity as a fraction of the second quantity2. Multiply by 100 to change the fraction into a percentage.

1 Write 42 as a percentage of 75.

STEP 1: 4275

STEP 2: 4275

100 56%

2 There are 30 students in a class. Six of the students are left-handed. What percentage of the students are left-handed?

STEP 1: 6

30STEP 2:

6

30100 20%

Percentage increase and percentage decrease

1 John’s income increases from $20 000 a year to $23 000 a year. Calculate the percentage increase in his income.

STEP 1:

% increase =

increaseoriginal value

100% % decrease =

decreaseoriginal value

100%

Increase = 23 000 – 20 000 = 3000

STEP 2: % increase =

increaseoriginal value

100%

300020000

100%

= 15%

2 The population of a village decreases from 785 to 634. Calculate the percentage decrease in the population.

STEP 1: Decrease = 785 – 634 = 151

STEP 2:

151785

100%

= 19.2%

% decrease =

decreaseoriginal value

100%

Percentage profit and loss

1 A car salesman buys a car for $15 000 and sells it for $17 000. Calculate the percentage profit.

STEP 1:

% profit =

profitoriginal cost

100% % loss =

lossoriginal cost

100%

Profit = 17 000 – 15 000 = 2000

STEP 2: % profit =

profitoriginal cost

100%

2000 100%15000

= 13.3%

2 Cara buys a bike for $250 and then sells it one year later for $180. Calculate the percentage loss.

STEP 1: Loss = 250 – 180 = 70

STEP 2: % loss =

lossoriginal cost

100%

70250

100%

= 28%