Fractions: Addition, Subtraction, Multiplication and Division
Fractions describe equal parts of a whole and are used in sharing, measurement and comparison.
Parts of a fraction
In a fraction a/b, a is the numerator and b is the denominator. The denominator cannot be zero. Fractions may be proper, improper or mixed numbers. Equivalent fractions have the same value, for example 1/2 = 2/4.
Operations
- To add or subtract, express fractions with a common denominator, then operate on the numerators.
- To multiply, multiply numerators and denominators, then simplify.
- To divide by a fraction, multiply by its reciprocal.
Worked examples
- 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
- 3/4 − 1/8 = 6/8 − 1/8 = 5/8.
- 2/3 × 3/5 = 2/5; and 4/7 ÷ 2/3 = 4/7 × 3/2 = 6/7.
Practice
- Compare 5/8 and 3/4.
- Calculate 2/5 + 7/10 and 5/6 − 1/4.
- Evaluate 3/8 × 4/9 and 5/12 ÷ 10/9.
