Chapter 8: Working with FractionsClass 7 Mathematics — summary, notes, extra questions & NCERT solutions

Summary

This chapter develops multiplication and division of fractions with meaning. Multiplying a fraction by a whole number repeats it (\(\tfrac{2}{5}\times 3 = \tfrac{6}{5}\)), and multiplying two fractions uses Brahmagupta's rule \(\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}\), which you also see as the area of a rectangle with fractional sides. Common factors can be cancelled before multiplying to keep numbers small. A key insight is how the size of a product depends on the factors: multiplying by a number between 0 and 1 makes the product smaller than the other number, while multiplying by a number greater than 1 makes it larger. Division is turned into multiplication using the reciprocal: \(\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}\). When the divisor is between 0 and 1 the quotient is bigger than the dividend; when it is greater than 1 the quotient is smaller. The chapter is rich in history — Brahmagupta, Bhaskaracharya's Lilavati, and the Shulbasutra — and applies fractions to many everyday sharing and measuring problems.

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