Computation with integers

Working without a calculator

These exams are calculator-free, so written methods must be automatic: long multiplication (such as $823 \times 47$) and long division (such as $11856 \div 13$) both appear for full marks. Line up place values carefully, and estimate first — $800 \times 50 = 40000$ tells you instantly if your answer has slipped a column.

Word problems are usually one operation in disguise: rows of parking spaces means multiply; sharing potatoes into 3 kg bags means divide. Write the calculation, then answer in a sentence.

Order of operations

Work through BIDMAS: brackets first (innermost first when brackets are nested), then indices, then multiplication and division left to right, then addition and subtraction left to right.

$$5 + [21 - (5 \times 3)] \times 4 = 5 + 6 \times 4 = 29$$

Square brackets behave exactly like round ones — do the inside bracket first. Never work simply left to right.

Directed numbers

For adding and subtracting, think of a number line: adding a negative moves you down, subtracting a negative moves you up. So $-2 + (-8) + 6 = -10 + 6 = -4$.

For multiplying and dividing: same signs give a positive, different signs give a negative. An odd number of negative factors leaves the answer negative: $(-5)^3 = -125$.

A typical exam line mixes everything:

$$27 \div (-3) - 3 \times (-7) = -9 - (-21) = -9 + 21 = 12$$

Place value and ordering

Expect questions on writing an expanded numeral like $5 \times 10^3 + 6 \times 10^2 + 2 \times 10 + 1$ as a basic numeral ($5621$), and rounding to a given place — $23578$ to the nearest thousand is $24000$.

Ordering integers: the further left on the number line, the smaller, so $-15 < -3 < 0 < 2$. Descending order starts with the largest. For “insert $<$, $=$ or $>$” questions, fully evaluate each side first, then compare.