Chapter 8: Working with Fractions
We already add and subtract fractions. Now we multiply and divide them: by whole numbers and by other fractions. We see why the rules work using areas, learn when products and quotients get bigger or smaller, and solve real and historical problems, from tea cups to fountains and a famous joke in Līlāvatī.
In this chapter you will
- multiply fractions by whole numbers and by fractions
- use the area model and cancel common factors
- divide using reciprocals
- solve word problems with fractions
Topics
- Multiplication of Fractions NCERT 8.1
a/b × c/d = (a × c)/(b × d); cancel common factors first.
- Division of Fractions NCERT 8.2
The reciprocal of a/b is b/a; their product is 1.
- Some Problems Involving Fractions NCERT 8.3
"Of" means multiply; sharing equally means divide.
Key words
- Product
- the result of multiplying
- Reciprocal
- the fraction flipped: 3/5 ↔ 5/3
- Cancelling
- dividing a numerator and a denominator by a common factor before multiplying
- Dividend
- the number being divided
- Divisor
- the number we divide by
- Quotient
- the result of dividing
Summary
- a/b × c/d = (a × c)/(b × d), Brahmagupta's rule; cancel common factors first.
- The area of a rectangle with fraction sides is their product.
- To divide, multiply by the reciprocal of the divisor: a/b ÷ c/d = a/b × d/c.
- Multiplying by (or dividing by) a number between 0 and 1 makes things smaller (or bigger).