Number System and Arithmetic Operations
Number System and Arithmetic Operations
This domain tests signed integers, fractions, decimals and rational numbers. Questions ask you to simplify expressions, convert between forms, compare rational numbers and decide whether a decimal terminates.
Core rules
- Follow BODMAS: brackets, powers, then × and ÷ from left to right, then + and − from left to right.
- For fractions, a/b + c/d = (ad + bc)/bd; to divide, multiply by the reciprocal: a/b ÷ c/d = a/b × d/c.
- A rational number is p/q with q ≠ 0. In lowest terms, it has a terminating decimal exactly when q has no prime factor other than 2 and 5.
- Convert decimals by place value: 0.125 = 125/1000 = 1/8; 0.06 = 6/100 = 3/50.
- Compare a/b and c/d by cross-multiplying: compare ad and bc when b, d > 0.
Worked example
Simplify −3/4 + 0.6 ÷ 0.2 − (−1/2). First divide: 0.6 ÷ 0.2 = 3. The expression becomes −3/4 + 3 + 1/2, because subtracting −1/2 is adding 1/2. Use denominator 4: −3/4 + 12/4 + 2/4 = 11/4 = 2.75.
Traps
- Do not cancel a number that is added, not multiplied: (2+3)/4 is not 2/4 + 3.
- Two negatives: −5 − (−7) = 2, not −12.
- Line up decimal points when adding decimals; 0.6 × 0.3 = 0.18, not 0.018.
- A denominator like 6 gives 1/6 = 0.1666…, which does not terminate.