ICSE Class 7 Maths Chapter 09 Percent Percentage

Chapter 9

Percent And Percentage

Basic Concept

The word CENT means hundred.

Hence, the word percent means, per hundred or out of hundred.

The notation for percent is "%".

Thus, 5 percent = 5%.

To Express An Ordinary Given Statement As Percent

Steps: 1. Express the given statement as a fraction.

2. Convert this fraction into an equivalent fraction with denominator 100.

Example 1:

7 out of 35 children in a class are absent. Express this statement as a percent.

Solution:

7 out of 35 means \(\frac{7}{35} = \frac{1}{5}\) [Step 1]

\(= \frac{1}{5} \times \frac{20}{20}\) [Step 2]

\(= \frac{20}{100} = 20\%\) \(\Rightarrow\) 20% children are absent. (Ans.)

OR, directly: 7 out of 35 means \(\frac{7}{35} = \frac{7}{35} \times 100\% = 20\%\) (Ans.)

Therefore, to express a fraction or a decimal as percent, multiply it by 100 and in the same step write the sign of percent (%).

For example:

(i) \(\frac{4}{10} = \frac{4}{10} \times 100\% = 40\%\)

(ii) 0.3 = 0.3 \(\times\) 100% = \(\frac{3}{10} \times 100\% = 30\%\)

Conversely, to change a percent to a fraction or to a decimal, divide it by 100 and at the same time remove percent sign.

For example:

(i) \(\frac{3}{4}\)% = \(\frac{3}{4 \times 100}\) = \(\frac{3}{400}\) (as fraction) = 0.0075 (as decimal)

(ii) 12.5% = \(\frac{12 \cdot 5}{100}\) = \(\frac{1}{8}\) (as fraction) = 0.125 (as decimal) and so on.

To Express One Quantity As A Percent Of The Other

1. If necessary, convert the quantities into the same units.

2. Form the fraction with the number to be compared as numerator and the number with which it is to be compared as denominator.

3. Multiply the fraction obtained by 100 and at the same time write the percent sign (%).

Example 2:

Express 40 p as a percent of \(\text{₹}\) 6.

Solution:

Fraction = \(\frac{40 \text{ p}}{600 \text{ p}}\) = \(\frac{1}{15}\) [\(\text{₹}\) 6 = 600 p]

Hence, required percent = \(\frac{1}{15} \times 100\% = \frac{20}{3}\)% = \(6\frac{2}{3}\)% (Ans.)

Direct method:

40 p as percent of \(\text{₹}\) 6 = \(\frac{40}{600} \times 100\%\) [\(\therefore\) \(\text{₹}\) 6 = 600 p]

\(= \frac{20}{3}\)% = \(6\frac{2}{3}\)%

\(\therefore\) If two quantities x and y are in the same unit, then

x as percent of y = \(\frac{x}{y} \times 100\%\)

and, y as percent of x = \(\frac{y}{x} \times 100\%\)

Example 3:

A pudding is made of 400 g sugar, 200 g of eggs, 800 g of flour and 100 g of dry fruits. What percent of sugar is present in the whole pudding?

Solution:

Here, the total weight of the pudding = (400 + 200 + 800 + 100) g = 1500 g

Weight of sugar = 400 g

\(\therefore\) Percentage of sugar in the pudding = \(\frac{400}{1500} \times 100\% = 26\frac{2}{3}\)% (Ans.)

To Find Percentage Of A Quantity

1. 20% of 60 = \(\frac{20}{100} \times 60 = 12\)

2. 40% of 7.5 = \(\frac{40}{100} \times 7.5 = 3\) and so on.

Example 4:

In a class of 50 children, 10% are taking part in dramatics. How many children are not taking part?

Solution:

Since, 10% of 50 = \(\frac{10}{100} \times 50 = 5\)

Hence, 5 children are taking part and 50 - 5 = 45 are not taking part. (Ans.)

Alternative method:

If 10% of the children are taking part

\(\Rightarrow\) (100 - 10)% = 90% are not taking part

\(\therefore\) Number of children not taking part = 90% of 50

\(= \frac{90}{100} \times 50 = 45\) (Ans.)

Teacher's Note

Understanding percentages helps in real-life situations like calculating discounts while shopping, understanding interest on savings, or finding what portion of your daily time is spent on different activities.

This is a preview of the first 3 pages. To get the complete book, click below.