Proportional Reasoning-1

About this chapter

Proportional Reasoning-1 is the seventh chapter of Class 8 Ganita Prakash Part 1. It introduces the idea of a ratio, of two ratios being proportional, and of using proportional reasoning to solve everyday problems. The chapter opens with five tiger photographs of different sizes and asks why three look similar but two look distorted — the answer is that width and height have 'changed by the same factor' only in the similar set. From this picture-based start the chapter builds six ideas: ratio as a : b with terms; reducing a ratio to simplest form using HCF; the proportion symbol :: and the rule that two ratios are proportional when their simplest forms match; problem-solving with proportional reasoning (Kesang's lemonade, Nitin and Hari's compound wall, Neelima's age); Trairasika or the Rule of Three from Aryabhata (199 CE) with cross multiplication ad = bc; sharing a quantity x in the ratio m : n using x/(m+n) groups; and unit conversions including the Fahrenheit-Celsius formula. CTET Paper 2 Mathematics tests this chapter through ratio simplification, finding the fourth proportional, sharing in a given ratio, and pedagogy items on the 'same factor' idea. The four tests — Practice 15, Quiz 15, Hard 15, Mastery 30 — cover all six ideas at CTET depth and difficulty.