Fractions
What the exam tests
Fractions checks equivalence, simplification, comparison and the four operations with proper fractions, improper fractions and mixed numbers. It also tests finding a fraction of a quantity.
Core rules
- Equivalent fractions are made by multiplying or dividing the numerator and denominator by the same non-zero number.
- Simplify by dividing by the highest common factor. For example, 18/24 ÷ 6 = 3/4.
- To add or subtract, use a common denominator. For different denominators, use the lowest common multiple.
- To multiply, multiply numerators and denominators separately. To divide, multiply by the reciprocal of the divisor.
- Change a mixed number to an improper fraction before multiplying or dividing: 2 1/3 = 7/3.
Worked example
Work out 2/3 + 3/4. The lowest common multiple of 3 and 4 is 12. Convert: 2/3 = 8/12 and 3/4 = 9/12. Add the numerators: 8/12 + 9/12 = 17/12. Since 17/12 is improper, write it as 1 5/12. The answer is already in simplest form.
Traps that cost marks
Never add denominators: 2/3 + 3/4 is not 5/7. Do not forget to convert a whole number to a fraction, for example 2 − 1/3 = 6/3 − 1/3 = 5/3. When dividing, only the divisor is turned upside down. Always simplify the final answer, and check that a fraction of a quantity uses multiplication, not addition.