NCERT Solutions Class 8 Maths Ganita Prakash Chapter 7 — Proportional Reasoning-1#

Chapter 7 of Ganita Prakash Part I is about ratios and proportions: when two ratios are proportional, similar shapes, the rule of three (trairāśika), dividing a quantity in a given ratio, and converting between units.

Figure it Out — Page 165 Figure it Out — Page 170 Figure it Out — Page 175 Figure it Out — Page 176

Exercises#

Figure it Out — Page 165 — Proportional ratios, similar rectangles, brick patterns, body ratios (7 questions)
Figure it Out — Page 170 — The Earth’s distance in a week, bricks for a house (2 questions)
Figure it Out — Page 175 — Dividing in a ratio, mixtures of paint, acid and idli batter (5 questions)
Figure it Out — Page 176 — Rule of three and unit conversions, a Lilavati problem, the ₹10 coin (12 questions)

What you will learn#

$a : b$ and $c : d$ are proportional ($a : b :: c : d$) when both terms change by the same factor, that is when $ad = bc$.
Using the rule of three to find a missing term.
Dividing a quantity in a given ratio.
Converting units of length, area and volume.

Key formulas and results#

$a : b :: c : d$ exactly when $ad = bc$.
Dividing $x$ in the ratio $m : n$: the parts are $\dfrac{m}{m + n} \times x$ and $\dfrac{n}{m + n} \times x$.
1 acre $= 43{,}560$ sq ft; 1 litre $= 1000$ mL.

Read and revise#

NCERT Class 8 Maths Chapter 7 (PDF) — the Ganita Prakash Part I chapter itself.
All Class 8 Maths chapters from Ganita Prakash Part I and Part II.

Frequently asked questions#

How many questions are in Class 8 Maths Chapter 7?

Four Figure it Out sets — pages 165–167 (7 questions), pages 170–171 (2 questions), page 175 (5 questions) and pages 176–177 (12 questions). Every question is solved step by step here.

How do you divide ₹4,500 in the ratio 2 : 3?

There are $2 + 3 = 5$ parts, so one part is $4500 \div 5 = 900$. The shares are $2 \times 900 = ₹1800$ and $3 \times 900 = ₹2700$.

7. Proportional Reasoning-1