Summary
Chapter 10 of Class 8 maths, "Proportional Reasoning-2", extends proportional reasoning concepts by teaching ratios with multiple terms, how to divide quantities in given ratios, pie chart construction using proportional angles, and inverse proportions where quantities change in opposite directions.
This chapter builds on proportional relationships by introducing ratios with more than two terms (e.g., 8 : 4 : 2 : 1), and teaches how to divide a whole quantity in a given ratio using a systematic method. Students learn to construct pie charts by calculating angles proportional to data values, and explore inverse proportions where one quantity increases as another decreases by the same factor, with the relationship xy = k.
Key points & formulas
- 01Two ratios a : b and c : d are proportional if a × d = b × c (cross-multiplication test)
- 02Representative Fraction (RF) on maps shows the ratio between map distance and actual geographical distance (e.g., 1 : 60,00,000 means 1 cm on map = 60 km on ground)
- 03Ratios with multiple terms (a : b : c : d) are proportional if all terms scale by the same factor
- 04To divide a quantity x in ratio p : q : r : s, each part is x × (term / sum of all terms)
- 05Pie chart angles are proportional to data: angle = (value / total) × 360°
- 06Inverse proportions: when one quantity increases by factor n, the other decreases by factor 1/n, with xy = k (constant product)
- 07Direct proportion: quotient remains constant (x₁/y₁ = x₂/y₂). Inverse proportion: product remains constant (x₁y₁ = x₂y₂)
Frequently asked questions
01What is Proportional Reasoning-2 in Class 8 maths?
It is Chapter 10 which extends basic proportion concepts to include ratios with multiple terms, dividing quantities in given ratios, pie chart construction using proportional angles, and inverse proportions where quantities change in opposite directions.
02How do you check if two ratios are proportional?
Use the cross-multiplication method: two ratios a : b and c : d are proportional if a × d = b × c. For example, 6 : 3 and 4 : 2 are proportional because 6 × 2 = 12 and 3 × 4 = 12.
03What is a Representative Fraction on a map?
It is the ratio between a distance on the map and the actual geographical distance on the ground. For example, RF 1 : 60,00,000 means 1 cm on the map equals 60,00,000 cm (60 km) in actual distance.
04How do you divide a quantity in a given ratio?
Add all terms in the ratio, then multiply the quantity by each term divided by the sum. For example, to divide 110 units in ratio 1 : 1.5 : 3, the sum is 5.5, so the parts are 110 × (1/5.5) = 20, 110 × (1.5/5.5) = 30, and 110 × (3/5.5) = 60.
05What is the difference between direct and inverse proportion?
In direct proportion, quantities change by the same factor (x₁/y₁ = x₂/y₂). In inverse proportion, when one quantity increases by factor n, the other decreases by factor 1/n, maintaining a constant product (x₁y₁ = x₂y₂ = k).
More chapters in Ganita Prakash
This is the complete Ganita Prakash Chapter 10 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 8 textbooks.
Read offline with notes, solutions & mock tests
CBSE Prepmaster — free on iOS & Android