Class 6 Mathematics

Chapter 12: Ratio and Proportion

STAGE 0: Foundation

In daily life, we compare quantities 😊

Examples:

• Number of boys and girls in a class
• Sugar and tea in a recipe
• Distance and time

Such comparison is done using ratio and proportion.

STAGE 1: Concepts Explained

Ratio

A ratio compares two quantities of the same kind.

It is written using the symbol :

Example:

Ratio of boys to girls = 3 : 2

Simplest Form of a Ratio

A ratio is said to be in simplest form when its terms have no common factor other than 1.

Example:

6 : 4 = 3 : 2

Proportion

When two ratios are equal, they are said to be in proportion.

Example:

2 : 4 = 4 : 8

Direct Proportion

If one quantity increases and the other also increases, they are in direct proportion.

Example:

More distance → More time

STAGE 2: Solved Examples

Example 1:
Write the ratio of 10 and 20.

Solution:
10 : 20 = 1 : 2

Example 2:
Check whether 3 : 5 and 6 : 10 are in proportion.

Solution:
3/5 = 6/10 = Yes, they are in proportion.

Example 3:
If 2 notebooks cost ₹20, what is the cost of 4 notebooks?

Solution:
2 notebooks → ₹20
4 notebooks → ₹40

STAGE 3: Practice Questions

1. Write the ratio of 12 and 18 in simplest form.
2. Write the ratio of boys to girls if there are 8 boys and 4 girls.
3. Are 4 : 6 and 10 : 15 in proportion?
4. If 5 pens cost ₹25, what is the cost of 10 pens?
5. Give one example of direct proportion from daily life.

STAGE 4: Quick Revision

• Ratio compares two quantities
• Use : symbol to write ratio
• Proportion means equal ratios
• Direct proportion increases together

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Shaktimatha CBSE Learning
Class 6 Mathematics – Learn Without Fear