Number and Operations
What you must understand
Candidates need secure place value up to at least seven digits, the four operations with whole numbers, fractions, decimals and percentages, rounding, factors and multiples, and order of operations. You should be able to convert freely between fractions, decimals and percentages, find equivalent fractions, and compare numbers of different forms. Divisibility rules for 2, 3, 5, 9 and 10 save time, and knowing that a percentage is simply a fraction with denominator 100 unlocks most word problems.
Traps to watch
- Order of operations: work brackets first, then multiplication and division left to right, then addition and subtraction left to right. Many candidates add before multiplying.
- Remainders in division: a remainder must be smaller than the divisor. In sharing problems, decide whether the remainder is discarded, rounded up, or kept.
- Decimal alignment: line up decimal points before adding or subtracting; count decimal places when multiplying.
- Percentage of a quantity: find 10% first, then build up. Do not confuse "increase by 20%" with "multiply by 20".
- Fraction of a set: the whole must be the correct total, not the part given.
Worked example
A shop sells a bag for P240. The price is reduced by 15%. What is the new price?
10% of P240 = P24, so 5% = P12. Therefore 15% = P24 + P12 = P36. New price = P240 − P36 = P204.
Rule of thumb: when a question mixes fractions, decimals and percentages, convert everything to the same form before calculating.