Proportional Reasoning-1 — Class 8 Mathematics

This chapter introduces ratios and proportional reasoning through similar images. Two images look similar when their width and height change by the same factor — a multiplicative relationship rather than an additive one. A ratio means for every units of one quantity there are units of another; reducing it by dividing both terms by their HCF gives its simplest form. Two ratios are proportional, written , when their simplest forms match, equivalently when cross-multiplication gives . This Rule of Three, known to Aryabhata as the relation among pramana, phala and ichchha, finds an unknown fourth quantity: . The chapter applies proportional reasoning to recipes, maps, prices and speeds, and to sharing a whole in a given ratio , where the parts are and . It also covers unit conversions and warns that adding or subtracting the same number from both terms of a ratio does not preserve proportionality.