CBSE Class 8 Maths Chapter 7 Proportional Reasoning 1 Notes

Proportional Reasoning is an important mathematics concept that helps you compare quantities, understand ratios, and solve practical problems. It explains how two ratios can represent the same relationship when reduced to their simplest form. You also learn to use the rule of three and cross multiplication to calculate unknown values. 

The chapter includes examples related to meals, travel distance, and lemonade preparation, making the concepts easier to understand. It also introduces useful unit conversions for length, area, volume, and temperature. These notes support quick revision, improve problem-solving skills, and help you to apply proportional reasoning confidently in examinations and everyday situations.

Proportional Reasoning 1 Class 8 Notes

A ratio compares two quantities, written as a : b.

Example:

• Width to height in Image A is 60 : 40.

Proportional Ratios (in simplest form):

• A: 60 : 40 = 3 : 2

• C: 30 : 20 = 3 : 2

• D: 90 : 60 = 3 : 2

Non-Proportional:

• B: 40 : 20 = 2 : 1

• E: 60 : 60 = 1 : 1

If different ratios simplify to the same form, they are said to be proportional.

Simplest Form of Ratios

To simplify a ratio, divide both terms by their Highest Common Factor (HCF).

Example:

• 60 : 40 → HCF = 20 → Simplest form = 3 : 2

• 90 : 60 → HCF = 30 → Simplest form = 3 : 2

So, 60 : 40 :: 90 : 60 means both ratios are proportional.

The symbol “::” is used to indicate proportionality.

Rule of Three (Trairasika)

If a : b :: c : d, then:

d = (b × c) / a

Example: Midday Meal

• 120 students : 15 kg

• 80 students : ?

80 is 2/3 of 120.

Therefore:

15 × 2/3 = 10 kg rice needed

Example: Travel Distance

• 150 min : 90 km

• 240 min : ?

Using cross multiplication:

x = (240 × 90) / 150

x = 144 km

Problem Solving Using Proportional Reasoning

Example 1: Check if 3 : 4 and 72 : 96 are proportional

Simplify:

72 : 96 = 3 : 4

Hence, they are proportional.

Example 2: Lemonade Mixing

• 6 glasses : 10 spoons

• To make 18 glasses, multiply both quantities by 3.

Therefore:

18 glasses : 30 spoons

Unit Conversions

Length

• 1 metre = 3.281 feet

Area

• 1 square metre = 10.764 square feet

• 1 hectare = 10,000 square metres = 2.471 acres

• 1 acre = 43,560 square feet

Volume

• 1 mL = 1 cc

• 1 litre = 1,000 mL or 1,000 cc

Temperature

°F = (9/5 × °C) + 32

°C = 5/9 × (°F − 32)

Proportional Reasoning 1 Notes PDF Class 8 

Class 8 Proportional Reasoning 1 Notes PDF explains ratios, proportional relationships, the rule of three, cross multiplication, and common unit conversions through simple examples. 

 These notes help you understand key concepts, practise problem-solving, and revise efficiently for examinations. Check below for the PDF and use it for quick learning, regular practice, and better preparation. 

Class 8 Proportional Reasoning 1 notes PDF