Fractions and Percentages
Fractions and percentages are two ways to write the same amount. To turn a fraction into a percentage, make the denominator 100. A percentage always means out of 100.
Video Lesson
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Flashcards
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What Is a Percentage?
- A percentage means “out of 100” (e.g. .
- It is another way of writing a fraction with denominator 100.
Converting Fractions to Percentages
- Change the fraction so the denominator is 100. For example, .
- You can do this by expanding or simplifying the fraction.
Finding a Percentage of a Total
- To find a percentage, divide the part by the total and multiply by 100 (e.g. .
- All parts together should add up to (e.g. .
Practice Questions
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Which of these percentages is equal to ?
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means . To turn a fraction or decimal into a percentage, multiply by 100: . So .
What is as a fraction in its simplest form?
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'Per cent' means 'out of 100', so is . Divide the numerator and denominator by their highest common factor, 20: .
A school has 30 teachers, and 12 of them teach science. What percentage of the teachers teach science?
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Write the science teachers as a fraction of all the teachers, then multiply by 100.
, and .
So of the teachers teach science.
Check: of 30 is 3, so of 30 is . ✓
A sports team played 45 games and won 27 of them. What percentage of the games did they win?
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Write the games won as a fraction of all the games played, then multiply by 100.
, and .
So the team won of their games.
Check: of 45 is 4.5, so of 45 is . ✓
A company sells 120 items in a month, and 96 of them are on sale. What percentage of items sold were on sale?
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Write the sale items as a fraction of all the items sold, then multiply by 100.
, and .
So of the items sold were on sale.
Check: of 120 is 12, so of 120 is . ✓
What fraction represents in its simplest form?
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A percentage means 'out of 100', so .
The highest common factor of 120 and 100 is 20, so divide top and bottom by 20:
.
Because is more than , the answer is correctly bigger than 1: .
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Interactive Activity
Practise converting fractions to percentages by finding equivalent fractions
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Frequently asked questions
The questions students bump into most on this topic
Per cent means out of one hundred, so a percentage is a fraction with 100 as its denominator: 70% is 70 out of 100, which simplifies to 7/10, and 1% is one hundredth. That is the only difference between the two: every percentage can be written as a fraction and every fraction as a percentage.
Change the fraction so its denominator is 100; the numerator is then the percentage. If the denominator divides into 100, multiply: 6/25 becomes 24/100 by multiplying top and bottom by 4, so 6/25 = 24%. If the denominator is bigger than 100, divide instead: 15/300 becomes 5/100 by dividing both by 3, so it is 5%.
Write the percentage over 100, then simplify. 70% is 70/100, and dividing top and bottom by 10 gives 7/10. 20% is 20/100, which simplifies to 1/5. If the percentage is over 100, the fraction is bigger than one whole: 120% is 120/100, or 6/5.
Write the first number as a fraction of the total, then change the denominator to 100. A club has 8 footballs and 12 basketballs, 20 balls in all. The footballs are 8/20; multiply top and bottom by 5 to get 40/100, so 40%. The basketballs are 12/20 = 60/100 = 60%, and the two parts add up to 100%.
3/5 is 60%. Multiply the top and bottom by 20 so the denominator becomes 100: 3/5 = 60/100, and 60 out of 100 is 60%. In the same way, 2/5 = 40/100 = 40%, and 1/5 = 20%. Any fraction whose denominator divides into 100 can be converted this way.
Say that per cent means out of 100, then use a 100-square grid: colour 70 squares and that is 70%, which is the same as 7 out of every 10. Shop sales are the best practice: a sign saying 50% off means half, and 25% off means a quarter.
What's next?
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