Proportional Reasoning-2 — Class 8 Mathematics

Building on the first proportional reasoning chapter, this one extends ratios to more than two terms and introduces inverse proportion and pie charts. Ratios like keep their proportion when every term scales by the same factor, and dividing a whole among parts gives each part as . Map scales (Representative Fractions like ) connect map distance to real distance. A pie chart turns a ratio into slices by dividing in that ratio. The major new idea is inverse proportion: two quantities and are inversely proportional when their product is constant, ; as one increases by a factor , the other decreases by . This models speed-and-time, workers-and-days and pumps-and-hours problems, where . The chapter contrasts this with direct proportion, where the quotient stays constant, and uses both to solve everyday work-rate problems.