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YOUR STUDY SPACE · CBSE

Fractions in Disguise — Class 8 Mathematics

Ganita Prakash Part 2 · Chapter 1

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Chapter summary

This chapter reveals percentages as fractions in disguise. The word per cent comes from the Latin per centum, meaning out of a hundred, so a percentage is simply a fraction with denominator : . Any fraction can be expressed as a percentage by finding an equivalent fraction with denominator , for example , or by multiplying the fraction by . Conversely, a percentage is converted back to a fraction or decimal by dividing by . The chapter shows how percentages let us compare proportions on a common scale even when the underlying totals differ, which is exactly why they are so widely used in marks, discounts and statistics. Finding a percentage of a quantity means taking that fraction of it, so of is . These tools connect fractions, decimals and percentages into a single flexible language for describing parts of a whole.
Percentages as fractionsExpressing fractions as percentagesConverting between fractions, decimals and percentagesFinding a percentage of a quantityComparing proportions

Key ideas & terms

Per cent
A fraction with denominator ; the symbol means out of every hundred.
Percentage
A way of writing a proportion as parts per hundred, e.g. .
Equivalent fraction
A fraction of equal value with a different denominator, used to reach denominator .
Fraction-to-percent
Multiplying a fraction by (or scaling its denominator to ) to express it as a percentage.
Percent of a quantity
Taking that fraction of the quantity; of equals .
Common scale
The benefit of percentages: proportions from different totals can be compared on a base of .

Extra questions & answers

What does the symbol mean?

It means per cent, or out of every hundred, so is out of .

Express as a percentage.

Scale to denominator : .

How do you turn any fraction into a percentage?

Multiply it by , or find an equivalent fraction with denominator .

What is of a quantity ?

It is .

Convert to a fraction in simplest form.

.

Where does the word per cent come from?

From the Latin per centum, meaning by the hundred or out of a hundred.

Express as a percentage.

.

Why are percentages useful for comparison?

They place all proportions on a common base of , so totals of different sizes can be compared.

Convert to a percentage.

Multiply by : .

What percentage is ?

It equals .