Mathematics Notes for Class 6 Ratio And-Proportion

Ratio and Proportion

Welcome to the chapter on Ratio and Proportion for Class 6. In this chapter, you will learn how to compare quantities using ratios and solve problems using proportions. By the end of this chapter, you will be able to use ratios and proportions in real-life situations and solve word problems confidently!

Introduction

Ratio and proportion are ways to compare numbers and quantities. They help us understand how much bigger, smaller, or equal one thing is compared to another.

What is a Ratio?

A ratio is a way to compare two or more quantities of the same kind by division. It shows how many times one quantity is compared to another.

Example: If there are 3 apples and 2 oranges, the ratio of apples to oranges is 3:2.
Ratios can be written as 3:2 or 3/2.

Simplifying Ratios

Ratios can be simplified just like fractions. Divide both numbers by their greatest common factor.

Example: 6:9 can be simplified to 2:3 (divide both by 3).

What is Proportion?

Proportion means that two ratios are equal. It is used to show that two pairs of numbers have the same relationship.

Example: 2:3 :: 4:6 (read as "2 is to 3 as 4 is to 6")
If 2/3 = 4/6, then the ratios are in proportion.

Solving Problems Using Proportion

Proportion helps us solve problems where we need to find an unknown quantity.

Example: If 5 pencils cost ₹10, how much do 10 pencils cost?
Set up the proportion: 5/10 = 10/x
Solve for x: x = 20

Word Problems

Use ratio and proportion to solve real-life problems. Read the question, set up the ratio or proportion, and solve.

Example: A recipe needs 2 cups of flour for 4 cookies. How much flour is needed for 12 cookies?
Set up the proportion: 2/4 = x/12 → x = 6 cups

Fun Activity: Ratio Hunt!

Look around your home or classroom. Find things you can compare using ratios, like boys to girls, red to blue books, or apples to bananas.

Summary

Ratio compares two or more quantities.
Proportion shows that two ratios are equal.
Use ratios and proportions to solve word problems.

Practice Questions

Write the ratio of 8 boys to 12 girls.
Simplify the ratio 15:25.
Are the ratios 3:4 and 6:8 in proportion?
If 7 apples cost ₹21, how much do 3 apples cost?
A bag has 5 red balls and 10 blue balls. What is the ratio of red to blue balls?

Challenge Yourself

Make your own word problem using ratio and proportion.
Find three examples of ratios in your daily life.

Did You Know?

Ratios are used in maps, recipes, and even sports!
Proportion helps in scaling drawings and models.

Glossary

Ratio: A way to compare two quantities.
Proportion: When two ratios are equal.
Simplify: To make a ratio smaller by dividing both numbers.
Quantity: An amount or number.

Answers to Practice Questions

8:12 or 2:3 (simplified)
3:5
Yes, because 3/4 = 6/8
₹9
5:10 or 1:2 (simplified)

Practice ratio and proportion every day to become a math expert!

Mathematics Class 6 - Ratio And-Proportion Notes