CBSE Class 7 Mathematics – 10. Percentage (Notes)

Notes on Percentage

Learning Goal

1. Percentage
2. Converting fraction or decimals numbers into percentage
3. Converting Percentage into fractions or Decimals
4. Converting percentage into ratio
5. Converting ratio into percentage

Use of Percentages

Interpreting percentages

Converting percentages to “How many”.

Ratios to percent

Increase or decrease as Percent

Profit or loss percentage

How to find SP if CP and profit or loss % is given?

How to find CP if SP and profit or loss % is given?

Percentage

The percentage is another way of comparisons.

The percentage is the numerator of the fraction with the 100 denominators.

Symbol of Percentage

Example

What is the percentage of boys and girls in the class of 100 students if the number of boys is 55 and the number of girls is 45?

Solution

Percentage if the total is not a hundred

If the total number of quantities is not hundred i.e. the denominator is not hundred then to find the percentage, we need to make the denominator 100.

Example

Out of 4 bees, 2 are going right and 2 are going left. So what percentage of bees is going right?

Solution

Unitary Method

Out of 4 bees, the number of bees going right are 2. Hence, out of 100, the number of bees going right is

By making denominator 100

Out of 4 bees, the number of bees going right is 2.

Converting fractional numbers to percentage

Multiply the fraction by 100%.

Example

Out of 15 fishes, 5 are red. What is the percentage of the red fishes?

Solution

Converting decimals to percentage

Multiply the decimals by 100%.

Example

Convert 0.65 into a percentage.

Solution

Multiply the decimal with the 100%.

Converting Percentage to fractions or Decimals

We can reverse the above process to convert the percentage into fraction or decimal.

Parts always add to give a whole

If we know the one part of a whole then we can find the other part because all the parts together form a whole or 100%.

Example

If there are 25 men in the office of 100 employees then the remaining 75 would be women.

This means that if 25% are men the (100% – 25%) = 75% are women.

Fun with estimation

With the help of percentage, we can estimate the parts of an area.

Example

What percent of the given figure is shaded?

Solution

First, we have to find the fraction of the shaded portion.

Use of Percentages

Interpreting percentages

To use the percentages in real life we must be able to interpret the percentage.

Example

 If we say that Seema is spending 20% of her income then it means that Seema is spending Rs. 25 out of every Rs. 100 she earns.

Converting percentages to “How many”.

Example

If 20% of students get a distinction out of 45 students in a class, then how many students got the distinction?

Solution

The number of students got distinction = [20/100] × 45 = 9.

Hence, 9 students out of 45 got the distinction.

Ratios to percent

Example

If the profit of Rs. 2500 is divided among three partners in such a way that A, B and C got the two parts, three parts and five parts of profit respectively. How much money will each get? What percent of the profit do they get?

Solution

The three partners are getting profit in the ratio of 2: 3: 5, so the total of the parts is

2 + 3 + 5 = 10

Increase or decrease as Percent

Sometimes we have to find the increase or decrease in certain quantities as a percentage. Like the increase in population, decrease in sale etc.

Example

The total marks of Charlie increased from 365 to 380 from last year’s result. Find the increase in percentage.

Solution

Original amount = Marks of Charlie last year = 365

Amount of change = increase in the number of marks = 380 – 365 = 15.

Therefore,