Class 6 Exam  >  Class 6 Notes  >  Mathematics Class 6 (Maharashtra Board)  >  Chapter Notes: Percentages

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.

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

  • 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

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)(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
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)
Hence, 20% of 80 = 16.
(b) 32% of 75
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)Hence, 32% of 75 = 24
(c) 45% of 80 days

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

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.
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)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
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)Thus, the required number
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)Hence, 160 is the required number whose 15% is 24.
(b) We have 36% of the required number = 117
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)Thus, the required number
Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)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 725Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

= 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

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

= 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

The document Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board) is a part of the Class 6 Course Mathematics Class 6 (Maharashtra Board).
All you need of Class 6 at this link: Class 6
30 videos|112 docs|15 tests

FAQs on Percentages Chapter Notes - Mathematics Class 6 (Maharashtra Board)

1. What are the different ways to express the same value in fractions, decimals, and percentages?
Ans.Fractions, decimals, and percentages are different ways to represent the same numerical value. A fraction shows a part of a whole, such as 1/2. A decimal represents that same value in a base-10 format, such as 0.5. A percentage expresses a fraction out of 100, so 1/2 can also be written as 50%. Understanding these conversions is essential for comparing values and solving various mathematical problems.
2. How do you convert a fraction to a percentage?
Ans.To convert a fraction to a percentage, you can follow these steps: First, divide the numerator (top number) by the denominator (bottom number). Then, multiply the result by 100. For example, to convert 3/4 to a percentage, you divide 3 by 4, which equals 0.75, and then multiply by 100 to get 75%. This means that 3/4 is equivalent to 75%.
3. What is the method for finding the percentage of a number?
Ans.To find the percentage of a number, you multiply the number by the percentage (expressed as a decimal). For example, to find 20% of 50, you convert 20% to a decimal (which is 0.20) and then multiply: 50 x 0.20 = 10. Therefore, 20% of 50 is 10.
4. Can you explain how to solve word problems involving percentages?
Ans.Solving word problems involving percentages typically requires careful reading and identifying the key information. Start by determining what the problem is asking for. Next, convert any necessary values into fractions or decimals if needed. Use the percentage formula (Percentage = (Part/Whole) x 100) to set up your equation and solve for the unknown. Make sure to double-check your work to ensure accuracy in calculations.
5. Why is it important to understand the relationship between fractions, decimals, and percentages?
Ans.Understanding the relationship between fractions, decimals, and percentages is crucial for various reasons. It helps in everyday situations like shopping discounts, calculating interest rates, and interpreting data. Additionally, in mathematics and scientific fields, the ability to convert between these forms enhances problem-solving skills and comprehension of different concepts, making it easier to analyze and compare information effectively.
Related Searches

study material

,

Summary

,

ppt

,

shortcuts and tricks

,

Free

,

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

,

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

,

Semester Notes

,

Objective type Questions

,

past year papers

,

video lectures

,

Viva Questions

,

Extra Questions

,

MCQs

,

Previous Year Questions with Solutions

,

Exam

,

Sample Paper

,

mock tests for examination

,

Percentages Chapter Notes | Mathematics Class 6 (Maharashtra Board)

,

pdf

,

Important questions

,

practice quizzes

;