ICSE Class 6 Maths Chapter 09 Percentage

Chapter 9

Percentage

Percent

Per means 'for every' or 'out of', and cent means 'hundred.' Thus, percent means 'for every hundred' or 'out of hundred.'

For example:

If in an examination for 100 marks, Geeta secured 83 marks; that means Geeta scored 83 percent marks.

Conversely, if in the same examination, Rohit secured 67 percent marks that means Rohit has got 67 marks out of 100.

The symbol for percent is %.

Percentage

Percentage is the numerator of a fraction with denominator 100.

For example: 60 out of 100 = \(\frac{60}{100}\) as fraction with denominator 100 = 60 as percentage, written as 60%.

Thus, when a fraction is so expressed that its denominator is 100, the corresponding numerator is called percentage.

\(\therefore\) (i) \(\frac{3}{100}\) = 3% (ii) \(\frac{7}{50}\) = \(\frac{7 \times 2}{50 \times 2}\) = \(\frac{14}{100}\) = 14% and so on

Infact, we do not follow any difference between percent and percentage strictly.

Example 1:

Express each of the following statements in the percentage form:

(i) 5 out of 20 eggs are bad.

(ii) 3 children in a class of 30 are absent.

Solution:

(i) 5 out of 20 eggs are bad means \(\frac{5}{20}\)

And \(\frac{5}{20}\) = \(\frac{5 \times 5}{20 \times 5}\) = \(\frac{25}{100}\) = 25% \(\therefore\) 25% eggs are bad. (Ans.)

(ii) 3 children out of 30 are absent is written as \(\frac{3}{30}\)

And \(\frac{3}{30}\) = \(\frac{1}{10}\) = \(\frac{10}{100}\) = 10% \(\therefore\) 10% children are absent. (Ans.)

Converting A Given Fraction Or Decimal Into Percentage (Percent Form):

Multiply the given fraction or decimal by 100 and at the same time write the sign of percentage.

For example:

(i) \(\frac{3}{4}\) = \(\frac{3}{4}\) \(\times\) 100% = 75% (ii) 0-225 = 0-225 \(\times\) 100% = 22-5% and so on.

In example 1 given above:

(i) 5 out of 20 are bad = \(\frac{5}{20}\) eggs are bad = \(\frac{5}{20}\) \(\times\) 100% eggs are bad = 25% eggs are bad.

(ii) 3 children in a class of 30 are absent = \(\frac{3}{30}\) children are absent = \(\frac{3}{30}\) \(\times\) 100% children are absent = 10% children are absent

Converting A Given Percentage Into A Fraction Or Decimal:

Remove the sign of percentage and at the same time divide by 100. Then reduce the resulting fraction obtained to its lowest terms or decimal as required.

For example:

(i) 25% = \(\frac{25}{100}\) = \(\frac{1}{4}\) or, 25% = \(\frac{25}{100}\) = 0-25

(ii) 37-5% = \(\frac{37 \cdot 5}{100}\) = \(\frac{375}{100 \times 10}\) = \(\frac{3}{8}\) or, 37-5% = \(\frac{37 \cdot 5}{100}\) = 0-375 and so on.

When a whole number is divided by 100, decimal point is placed just after two digits from the right. But when a decimal number is divided by 100, the decimal point is shifted two places to the left.

Teacher's Note

Understanding percentages helps you calculate discounts while shopping and understand interest rates on savings accounts.

Exercise 9(A)

1. Express each of the following statements in percentage form:

(i) 13 out of 20 (ii) 21 eggs out of 30 are good

2. Express the following fractions as percent:

(i) \(\frac{3}{200}\) (ii) \(\frac{5}{6}\) (iii) \(\frac{65}{80}\) (iv) \(\frac{2}{3}\)

3. Express as percent:

(i) 0-10 (ii) 0-02 (iii) 0-7 (iv) 0-15 (v) 0-032

4. Convert into fractions in their lowest terms:

(i) 8% (ii) 20% (iii) 85% (iv) 250% (v) \(12\frac{1}{2}\)%

5. Express as decimal fractions:

(i) 25% (ii) 108% (iii) 95% (iv) 4-5% (v) 29-2%

6. Express each of the following numbers as percent:

(i) 7 (ii) 2 (iii) 19-5 (iv) 5-37

Expressing One Quantity (Number) As A Percentage Of The Other:

Divide the first quantity by the second one and at the same time multiply the result by 100%.

For example:

(i) 20 kg as a percentage of 200 kg = \(\frac{20}{200}\) \(\times\) 100% = 10%

(ii) 60 paise as a percent of \(\text{₹}\) 3 = 60 paise as a percent of 300 paise = \(\frac{60}{300}\) \(\times\) 100% = 20%

1. Percent / percentage has no unit.

2. In order to express one quantity as a percentage of another quantity, the two quantities must have the same unit.

Finding Percentage (Percent) Of A Given Quantity:

Express the given percent as fraction and multiply by the given number.

For example:

25% of \(\text{₹}\) 500 = \(\frac{25}{100}\) \(\times\) \(\text{₹}\) 500 = \(\text{₹}\) 125 and 30% of 400 = \(\frac{30}{100}\) \(\times\) 400 = 120

Example 2:

In a class of 50 students, 40% are girls. Find the number of girls and number of boys in the class.

Solution:

No. of girls in the class = 40% of 50 = \(\frac{40}{100}\) \(\times\) 50 = 20 (Ans.)

No. of boys in the class = 50 - 20 = 30 (Ans.)

Alternative method:

When a class has 40% girls, it has (100 - 40)% boys, i.e. 60% boys.

\(\therefore\) No. of girls = 40% of 50 = \(\frac{40}{100}\) \(\times\) 50 = 20

and no. of boys = 60% of 50 = \(\frac{60}{100}\) \(\times\) 50 = 30 (Ans.)

Example 3:

A girl scored 60 out of 75 in English, 60 out of 90 in Mathematics, and 80 out of 100 in Science. Find girl's score as percentage:

(i) in Mathematics (ii) in all the three subjects (as a whole)

Solution:

(i) Percentage score in Mathematics = 60 out of 90 = \(\frac{60}{90}\) \(\times\) 100% = \(\frac{200}{3}\)% = \(66\frac{2}{3}\)% (Ans.)

(ii) Sum of the maximum marks of all the three subjects = 75 + 90 + 100 = 265 and total score in the three subjects = 60 + 60 + 80 = 200

\(\therefore\) Percentage score as a whole = \(\frac{200}{265}\) \(\times\) 100% = \(75\frac{25}{53}\)% (Ans.)

Teacher's Note

Calculating percentage scores helps you understand your academic performance across different subjects.

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