Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board) PDF Download

Introduction

• The given floor is divided into 100 smaller tiles, and the coloured square tiles represent a fraction of these 100 tiles.

• In this picture, there are 42 coloured square tiles. This means that 42 out of 100 squares are shaded.
• This can be expressed as 42/100 of the floor being coloured or 42 square tiles per hundred being coloured.
• When a fraction has 100 as its denominator, it is called a percentage.
• Therefore, 42 out of 100 can be written as 42 per cent, which is abbreviated as 42%.

To Convert Fractions, Decimals, and Percentages from One Form to Another

(i) To Convert a Fraction into a Percentage

Rule: To convert a fraction into a percentage, multiply by 100.

Example Calculations:

• 46/100 = (46 × 100)% = 46%
• 2/5 = (2 × 100)% = 40%
• 13/15 = (15 × 100)% = 86 2/3%

(ii) To Convert a Percentage into a Fraction

Rule: To convert a percentage into a fraction, divide by 100.

Example Calculations:

• 32% = 32/100 = 16/50 = 8/25
• 158% = 158/100 = 79/50 = 129/100
• 53/8% = 53/8 × 1/100 = 53/800
• 2.4% = 2.4 × 1/100 = 24/100 = 125/10

(iii) To Convert a Decimal into a Percentage

Rule: To convert a decimal into a percentage, multiply by 100 or shift the decimal point two places to the right.

Example Calculations:

• 0.37 = (0.37 × 100)% = 37%
• 18.54 = (18.54 × 100)% = 1854%

(iv) To Convert a Percentage into a Decimal

Rule: To convert a percentage into a decimal, divide by 100 or shift the decimal point two places to the left.

Example Calculations:

• 74% = 74/100 = 0.74
• 1842% = 1842/100 = 18.42

Finding the Percentage of a Number

The following examples will help you to understand the required procedure.

Example 1: Find: 
(a) 20% of 80 
(b) 32% of 75 
(c) 45% of 80 days

(a) 20% of 80

Hence, 20% of 80 = 16.
(b) 32% of 75
Hence, 32% of 75 = 24
(c) 45% of 80 days

Hence, 45% of 80 days = 36 days.

Example 2: What per cent of 80 is 60?

60 out of 80 is equivalent to the fraction 60 / 80.
Hence, 75% of 80 is 60.

To Find the Number Whose Percentage is Given

Example 3: Find the number whose:
(a) 15% is 24
(b) 36% is 117

(a) We have, 15% of the required number = 24
Thus, the required number
Hence, 160 is the required number whose 15% is 24.
(b) We have 36% of the required number = 117
Thus, the required number
Hence, 325 is the required number whose 36% is 117.

Word Problems

Example 4: In a school, there are 725 students. Out of these, 32 are girls. How many girls are there? Also, find the number of boys in the school.

Sol: 

Total number of students = 725

Number of girls = 32% of 725

= 232

Now, the number of boys can be calculated as by subtracting the number of girls from the total number of students.

Number of boys in the school = 725 - 232 = 493

Example 5: The population of a village is 3,250 out of them 52% are males. Find the number of males in the village. Also, find the number of females in the village.

Sol:

We know that 52% of the population is males. Let us find out the number.

Total population = 3,250

Males in the population = 52% of 3250

= 1690

Therefore, there are 1,690 males in the village.

To find out the number of females in the village, we simply subtract the number of males from the total population.

Number of females = 3250 - 1690 = 1560