Converting between fractions and percentages?
Worked examples: Converting between fractions and percentages
Adding fractions
Percentage means ‘parts of a hundred’.
When you work with percentage you are dealing with a special sort of fraction.
% = something
100
25% means 25 parts of every hundred parts.
8½% means 8½ parts of every hundred parts.
32.25% means 32.25 parts of every hundred parts.
Working out a percentage of something
What is 20% of $500? Multiply your percentage fraction by the amount.
20% of $500 = 20 x 500
100 1
= 20 x 5
= $100
Changing fractions and decimals to percentage
What is ¾ expressed in percentage terms?
A percentage is a fraction with a denominator of 100.
3 = 75 = 75%
4
100
(multiply numerator by 25.)
(multiply denominator by 25.)
Changing percentage to a fraction or decimal
Remember, a percentage figure is a fraction of a hundred.
80% = 80 = 4
100 5
(divide both numerator and denominator by 20 to simplify.)
80% = 80 = 4 = 0.8 (divide denominator into numerator to get a decimal fraction.)
100 5
Activity sheet: Converting between fractions and percentages
Page 1
Percentage problems
1.
If you are going to be paid 25% of a job worth $240, how much will you get?
2.
What is 5/8 expressed in percentage terms?
3.
What is 75% expressed as a decimal and a fraction?
4.
If the amount of chromium in stainless steel is 13% by mass, find out the mass of chromium in
2500kg of stainless steel. (Hint: find out 13% of the total mass.)
5.
From a batch of welds done on an automatic welding machine 10 were rejected. If the rejected
welds represent 8% of the total, how many welds were produced altogether? (Hint: work out what
1% of the total is first, then multiply this by 100 to find 100%.)
Check your responses with the answers below.
Answers
(1) $60
(2) 62.5%
(3) .75, 3/4
(4) 325kg
Activity sheet: Converting between fractions and percentages
(5) 125 welds
Page 2