Working with Fractions

Overview

This chapter develops skills with fractions: comparing them and adding, subtracting, multiplying and dividing them. Fractions describe parts of a whole.

Key concepts

• Proper, improper and mixed fractions.
• Equivalent fractions and lowest terms.
• Adding/subtracting needs a common denominator.
• Multiplying: multiply numerators and denominators.
• Dividing: multiply by the reciprocal.

Important formulae

• a/b × c/d = (a × c)/(b × d)
• a/b ÷ c/d = a/b × d/c
• a/b + c/b = (a + c)/b

Solved example

1. Find 2/3 × 3/4.
2. Multiply numerators and denominators: (2 × 3)/(3 × 4) = 6/12.
3. Simplify: 6/12 = 1/2.

Important questions

1. Add 1/2 + 1/3.
2. Find 5/6 − 1/4.
3. Divide 3/5 by 2.
4. Which is greater, 3/4 or 5/8?

Quick revision

Use a common denominator for + and −. Multiply straight across for ×, and flip the second fraction for ÷. Always reduce the answer to lowest terms.