Integers, Fractions and Decimals
Fractions
Pearson Edexcel International GCSE Mathematics A
Calculating with mixed numbers
| Operation | Rule |
|---|---|
| Mixed number to improper fraction | whole number × denominator + numerator, over the same denominator |
| Multiply | multiply the numerators and multiply the denominators, cancelling common factors |
| Divide | multiply by the reciprocal of the second fraction: turn it upside down |
| Add or subtract | write both fractions over a common denominator, then add or subtract the numerators |
Method: show that a mixed number calculation equals a given answer
- Write both mixed numbers as improper fractions.
- Divide: multiply by the reciprocal of the second fraction. Add or subtract: write both over a common denominator. Multiply: multiply numerators and denominators.
- Write the result as one fraction and simplify it.
- Convert it to the mixed number given in the question.
Write fractions in every line. Never write decimals in the working: they only check an answer afterwards.
Worked example: show that, dividing mixed numbers
Show that 313 ÷ 178 = 179
103 ÷ 158
= 103 × 815
= 8045 = 169
= 179
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