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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%