Chapter 8: Working with Fractions

A fraction is one of the most useful ideas in mathematics. Half a glass, three-quarters of a kilo, two-thirds of an hour , fractions show up wherever wholes split into equal parts.

In Class 6 you learned to add and subtract fractions. Now you will learn to multiply and divide them. The great Indian mathematician Brahmagupta ($\sim 628$ CE) gave clean rules for these operations more than a thousand years ago , and we still use them today.

You will see that multiplying fractions is much easier than adding them: no need for a common denominator. Multiply tops with tops, bottoms with bottoms, and simplify. Division is just multiplication by the reciprocal. Once you internalise the reciprocal idea, every fraction problem becomes solvable.

Finally, you will apply fractions to real-life situations , recipes, distances, splitting bills, finding "of" a quantity. By the end of the chapter, fractions will be your friends, not your foes.

What's inside

1. Recap and mixed numbers , proper, improper, mixed; switching between forms.
2. Multiplying fractions , top times top, bottom times bottom.
3. Reciprocal and dividing fractions , flip and multiply.
4. Fraction of a quantity , "$\tfrac{3}{4}$ of $20$" and similar.
5. Word problems with fractions , recipes, distances, money.

Key results

How to read this chapter

Always simplify before computing whenever possible. For example, $\tfrac{2}{3} \times \tfrac{9}{8}$ , cancel $2$ with $8$ and $3$ with $9$ first: $\tfrac{1}{1} \times \tfrac{3}{4} = \tfrac{3}{4}$. This saves arithmetic and avoids large numerators.