Page 119 - ICSE Math 6

9 Percentage

Key Concepts

• Percentage • Finding the Number from its Given Percentage
• Expressing One Quantity as a Percentage of the Other • Applications of Percentage
• Finding Percentage of a Given Quantity

Percentage
The word per cent is derived from a Latin word ‘per centum’ which means ‘by the hundred’. Thus, per
cent means ‘out of hundred’ or ‘for every hundred’. Per cent is denoted by the symbol ‘%’. Suppose
only 26 marbles out of 100 are green, then we say that, 26 per cent (written as 26%) of marbles are
green. Percentages can also be represented as fractions with the denominator 100.
85
For example, 85 out of 100 = = 85% (read as 85 percent)
100

Expressing One Quantity as a Percentage of the Other

To express ‘x’ as a percentage of ‘y’, follow the given steps.

Step 1: Convert x and y in the same unit, if needed.
x
Step 2: Multiply by 100%.
y
For example,
30
(a) 30 m as a percentage of 600 m = ×100% = 5% Try These
600
120 1. What is 10 cm as a percentage of
(b) 120 s as a percentage of 500 s = ×100% = 24% 1 m?
500 2. What is 1 kg 350 g as a percentage
Example 1: What percentage of ` 250 is ` 50? of 3 kg 375 g?
50
Solution: Required percentage = ×100% = 20%
250
Finding Percentage of a Given Quantity

Express the given percentage as a fraction with the denominator 100. Now, multiply this fraction by
the given number.
35 35
For example, 35% of ` 600 = × ` 600  35% = A
100 100 In general, A% = 100

= ` 210
Example 2: Out of 110 pens, 40% are blue and the rest are red. Find the number of red and blue
pens.
40
Solution: Number of blue pens = 40% of 110 = × 110 = 44
100
Number of red pens = 110 – 44 = 66

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