Percent and Percentage

ICSE Class 7 · Mathematics · Chapter 8

What this chapter covers

Percent means "per hundred" or "out of every hundred".

A percentage is a fraction whose denominator is 100, written as the numerator followed by the sign %.

The increase is the new value minus the original value, when the quantity has gone up.

The decrease is the original value minus the new value, when the quantity has gone down.

Percentage increase is the increase expressed as a percentage of the original value.

Percentage decrease is the decrease expressed as a percentage of the original value.

Percent means "per hundred"; the sign is %.
A percentage is a fraction with denominator 100, and also a ratio with second term 100.
The whole of any quantity is 100%; a percentage above 100 means more than the whole.
Percentage to fraction: write over 100 and reduce. Percentage to decimal: divide by 100, moving the point two places left.
Fraction or decimal to percentage: multiply by 100 and attach %.
Percentage of a quantity = (percentage)/(100) × quantity, in the quantity's unit.
One quantity as a percentage of another = (first)/(second) × 100%, with both in the same unit.
To find the whole from a known part, find 1% first and then multiply by 100.
Percentage increase or decrease = (change)/(original value) × 100%.
After a rise of r% the new value is (100 + r)% of the old; after a fall of r% it is (100 - r)% of the old.

Write 64% as a fraction in its lowest terms.

(64)/(100) = (16)/(25).

Write 0.09 and 1.4 as percentages.

0.09 = 9% and 1.4 = 140%.

Write 7.5% as a decimal and as a fraction in its lowest terms.

7.5% = 0.075 = (75)/(1000) = (3)/(40).

Change (11)/(20) and (5)/(6) into percentages.

(11)/(20) = 55%; (5)/(6) × 100% = (500)/(6)% = 83(1)/(3)%.

Arrange in descending order: 0.6, (5)/(8), 59%.

As percentages they are 60%, 62.5% and 59%, so the order is (5)/(8), 0.6, 59%.

Find 35% of ₹840.

(35)/(100) × 840 = 294, so ₹294.

What percentage of 2 hours is 24 minutes?

2 hours = 120 minutes, and (24)/(120) × 100% = 20%.

In a class of 40 pupils, 45% are girls. How many boys are there?

Boys are 55% of 40, which is (55)/(100) × 40 = 22 boys.