# Class 7 Percentage

Conversion of Percentage into a Fraction

Conversion of Fraction into a Percentage

Conversion of Percentage into Ratio

Conversion of Ratio into Percentage

Conversion of Percentage into Decimal

Conversion of Decimal into Percentage

How to Find Percentage of a Given Quantity

Expressing One Quantity as Percentage of Another Quantity

Finding Increasing or Decreasing of Percentage

## Introduction to Percentage

The word percent means, per hundred or out of hundred. In other word * Percentage* is the numerator of a fraction with denominator 100. The symbol of percent is

*. Let's see some examples where we use percentage in our day-to-day life.*

**%**
**Example 1.** John got 85 marks out of hundred marks, then we can say he got 85 percent marks. In fraction form we can write it as ^{85}⁄_{100}, here 85 is the mark secured and 100 is the total marks.

**Example 2.** 30 out of 50 students are girls in a school, then the percentage of girls in the school is ^{30}⁄_{50} = ^{30×2}⁄_{50×2} = ^{60}⁄_{100} = 60%.

## Conversion of Percentage into a Fraction

To convert percentage into fraction, we must replace the % sign with ^{1}⁄_{100}. Finally reduce the fraction to it's simplest form. Let's see some examples.

**Examples 1.** Express 20% in fraction form.

**Solution.** 20% = ^{20}⁄_{100} = ^{1}⁄_{5}

**Example 2.** Express 8.5% in fraction form.

**Solution.** 8.5% = ^{8.5}⁄_{100} = ^{85}⁄_{1000} = ^{17}⁄_{200}

## Conversion of Fraction into a Percentage

To convert a fraction into a percentage, we must multiply the fraction by 100 and write a % sign. Let's see some examples.

**Example 1.** Convert ^{2}⁄_{5} into fraction.

**Solution.** ^{2}⁄_{5} = ^{2}⁄_{5} × 100 = 40%

**Example 2.** Convert ^{2}⁄_{3} into fraction.

**Solution.** ^{2}⁄_{3} × 100 = ^{200}⁄_{3} = 66 ^{2}⁄_{3}%

## Conversion of Percentage into Ratio

To convert a percentage into a ratio, first we must convert into fraction to it's simplest form and then to a ratio. Let's see some examples.

**Examples 1.** Express 30% in fraction form.

Solution. 30% = ^{30}⁄_{100} = ^{3}⁄_{10} = 3 : 10

**Examples 2.** Express 32.5% in fraction form.

**Solution.** 32.5% = ^{32.5}⁄_{100} = ^{325}⁄_{1000} = ^{13}⁄_{40} = 13 : 40

**Examples 3.** Express 22 ^{2}⁄_{5}% in fraction form.

**Solution.** 22 ^{2}⁄_{5}% = ^{112}⁄_{5} ÷ 100 = ^{112}⁄_{5} × ^{1}⁄_{100} = ^{28}⁄_{125} = 28 : 125

## Conversion of Ratio into Percentage

To convert a ratio into percentage, first we have to convert the given ratio into a fraction and then convert into a percentage. Let's see some examples.

**Examples 1.** Express 2 : 5 in percentage form.

**Solution.** 2 : 5 = ^{2}⁄_{5} = ^{2}⁄_{5} × 100 = 40%

**Examples 2.** Express 5 : 8 in percentage form.

**Solution.** 5 : 8 = ^{5}⁄_{8} = ^{5}⁄_{8} × 100 = 0.625 × 100 = 62.5%

## Conversion of Percentage into Decimal

To convert a percentage into a decimal, first convert the percentage into a fraction and then convert fraction into decimal. Let's see some examples.

**Example 1.** Convert 72% into decimal.

**Solution.** 72% = ^{72}⁄_{100} = 0.72

**Example 2.** Convert 175% into decimal.

**Solution.** 175% = ^{175}⁄_{100} = 1.75

**Example 3.** Convert 38.5% into decimal.

**Solution.** 38.5% = ^{38.5}⁄_{100} = 0.385

## Conversion of Decimal into Percentage

To convert a decimal into a percentage, we have to multiply the decimal by 100 and put % sign. Let's see some examples.

**Example 1.** Convert 0.65 into percentage.

**Solution.** 0.65 = 0.65 × 100 = 65%

**Example 2.** Convert 2.75 into percentage.

**Solution.** 2.75 = 2.75 × 100 = 275%

## How to Find Percentage of a Given Quantity

To find a percentage of a given quantity, we must change the percentage into fraction and then multiply it by the given quantity. Let's see some examples.

**Example 1.** What is the value of 25% of 60?

**Solution.** 25% of 60 = ^{25}⁄_{100} × 60 = ^{60}⁄_{4} = 15

**Example 2.** Find the value of 15% of Rs. 80.

**Solution.** 15% of Rs. 80 = ^{15}⁄_{100} × 80 = ^{3}⁄_{20} × 80 = 3 × 4 = Rs. 12

## Expressing One Quantity as Percentage of Another Quantity

To express one quantity as a percentage of another same quantity, we must divide one quantity with the other quantity and then multiply the result with 100.

Let's see some examples.

**Example 1.** Express 25 as a percentage of 75.

**Solution.** Percentage = (^{25}⁄_{75} × 100)%

= 33 ^{1}⁄_{3} %

**Example 2.** Express 500 grams as percentage of 2.5 kg.

**Solution.** 2.5 kg = 2500 grams

Percentage = ^{500}⁄_{2500} × 100 = 20%

## Finding Increasing or Decreasing of Percentage

Let's see some examples to understand this.

**Example 1.** A cycle was costing Rs. 4500 last year, but this year it is costing Rs. 5000. Find the percentage increase in the price.

**Solution.** Original price = Rs. 4500

Rise in price = Rs. 5000 − Rs. 4500 = Rs. 500

Percentage increase = ^{500}⁄_{4500} × 100 = ^{100}⁄_{9} = 11 ^{1}⁄_{9}%

Hence, the price has increased by 11 ^{1}⁄_{9}%

**Example 2.** Price of orange per kilogram is Rs. 60 last year. This year orange price is Rs. 50 pr kilogram. Find the percentage decrease in price.

**Solution.** Original price = Rs. 60

Fall in price = Rs. 60 − Rs. 50 = Rs. 10

Percentage decrease = ^{10}⁄_{60} × 100 = ^{100}⁄_{6} = ^{50}⁄_{3} = 16 ^{2}⁄_{3}%

Hence, the price has decreased by 16 ^{2}⁄_{3}%

## Use of Percentage in Our Life

Let's see some real life problems on percentage.

**Example 1.** In a school of 200 students, 45% students are boys. How many girls are present in the school?

**Solution.** Boys percentage in the school is 45%.

Girls percentage in the school = 100 − 45 = 55%

Number of girls in the school = 55% of 200 = ^{55}⁄_{100} × 200 = 110

So, the number of girls present in the school is 110.

**Example 2.** Population of a country is 750000. It is forecasted that the population of the country will rise by 6% after 10 years. What will be the population of country after 10 years.

**Solution.** Population of the country = 750000

Rise in population = 6% of 750000

= ^{6}⁄_{100} × 750000 = 45000

Total population after 10 years = 750000 + 45000 = 795000

So, the population of the country after 10 years will be 795000.

**Example 3.** 25% of a number is 75, then find the number.

**Solution.** Let's assume the number is 'a'.

25% of a = 75

=> ^{25}⁄_{100} × a = 75

=> a = 75 × ^{100}⁄_{25}

=> a = 300

So, the number is 300.

**Example 4.** John bought a motor bike at a discount of 25% and he saved 15000. What was the price of the motorbike before discount?

**Solution.** Let's assume original price of the motorbike is 'q'.

q − 25% of q = 15000

=> q − ^{25q}⁄_{100} = 15000

=> ^{100q−25q}⁄_{100} = 15000

=> ^{75q}⁄_{100} = 15000

=> q = 15000 × ^{100}⁄_{75}

=> q = 20000

So, the original price of the motorbike is Rs. 20000

## Class-7 Percentage Test

## Class-7 Percentage Worksheet

## Answer Sheet

**Percentage-Answer**Download the pdf

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