Evaluate -8 + 3 × (-2). [2 marks]

SEAB Original-style practice: Evaluate 23 + 34 × 89, giving your answer as a fraction in its simplest form.

By the order of operations, multiplication comes before addition. Multiply first: 34 × 89 = 2436 = 23. Then add: 23 + 23 = 43, which is 113. Markers reward doing the multiplication before the addition, cancelling correctly, and giving the final fraction in its simplest form.

SingaporeMathsSyllabus dot point

How do we work confidently with integers, fractions, decimals and the order of operations?

Carry out the four operations on integers, fractions and decimals, apply the order of operations, and use approximation and estimation

A focused answer to the O-Level E-Maths outcome on numbers and the four operations. Integers, fractions and decimals, the order of operations, rounding to significant figures and decimal places, and sensible estimation.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to add, subtract, multiply and divide integers, fractions and decimals fluently, to apply the correct order of operations, and to round and estimate sensibly. These are the workhorse skills that every later topic depends on, so accuracy here protects marks everywhere else.

The answer

The four operations and negative numbers

The four operations are addition, subtraction, multiplication and division. With negative numbers, two rules carry most of the load. For multiplication and division, a pair of like signs gives a positive and a pair of unlike signs gives a negative, so $(-6) \times (-4) = 24$ but $(-6) \times 4 = -24$ . For addition and subtraction, subtracting a negative is the same as adding, so $7 - (-3) = 7 + 3 = 10$ .

Fractions

To add or subtract fractions, rewrite them over a common denominator, then combine the numerators:

\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}

To multiply, multiply numerators and denominators and cancel; to divide, multiply by the reciprocal of the second fraction:

\frac{3}{4} \div \frac{9}{8} = \frac{3}{4} \times \frac{8}{9} = \frac{24}{36} = \frac{2}{3}

Decimals

Treat decimals as ordinary numbers, lining up the decimal point for addition and subtraction. For multiplication, multiply as whole numbers then count the total decimal places. For division, shift both numbers so the divisor is a whole number, $4.5 \div 0.5 = 45 \div 5 = 9$ .

Order of operations

Work in the order: brackets, then indices (powers and roots), then multiplication and division left to right, then addition and subtraction left to right. The common memory aid is BIDMAS. So $3 + 4 \times 2^2 = 3 + 4 \times 4 = 3 + 16 = 19$ , not $49$ .

Rounding and estimation

To round to a given number of decimal places or significant figures, look at the next digit: if it is 5 or more, round up. Significant figures start from the first non-zero digit, so $0.004072$ to 2 significant figures is $0.0041$ . Estimation rounds each value to 1 significant figure to give a quick order-of-magnitude check on a calculator answer.

Examples in context

Example 1. Splitting a bill. Three friends share a $45.60 dollar meal equally, so each pays$ 45.60 \div 3 = 15.20$ dollars. Working with decimals and division accurately matters because money is rounded to two decimal places.

Example 2. Checking a calculator answer. A student computes $612 \times 39$ and reads $2386$ off the screen. A 1 significant figure estimate, $600 \times 40 = 24000$ , shows the displayed value is wrong by a factor of ten, prompting a recheck. Estimation is a cheap safeguard against keystroke errors.

Try this

Q1. Evaluate $-8 + 3 \times (-2)$ . [2 marks]

Cue. Multiply first: $3 \times (-2) = -6$ , then $-8 + (-6) = -14$ .

Q2. Write $0.030607$ correct to 3 significant figures. [1 mark]

Cue. Significant figures start at the first non-zero digit, $3$ , giving $0.0306$ .

Q3. Evaluate $\dfrac{7}{8} \times \dfrac{4}{21}$ , giving your answer as a fraction in its simplest form. [2 marks]

Cue. Multiply and cancel: $\dfrac{7 \times 4}{8 \times 21} = \dfrac{28}{168} = \dfrac{1}{6}$ .

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original3 marksEvaluate

\dfrac{2}{3} + \dfrac{3}{4} \times \dfrac{8}{9}

, giving your answer as a fraction in its simplest form.

Show worked answer →

By the order of operations, multiplication comes before addition.

Multiply first: $\dfrac{3}{4} \times \dfrac{8}{9} = \dfrac{24}{36} = \dfrac{2}{3}$ .

Then add: $\dfrac{2}{3} + \dfrac{2}{3} = \dfrac{4}{3}$ , which is $1\dfrac{1}{3}$ .

Markers reward doing the multiplication before the addition, cancelling correctly, and giving the final fraction in its simplest form.

Original4 marksA rectangular tile measures

24.6\ \text{cm}

13.8\ \text{cm}

. (a) Find its area, giving your answer to 3 significant figures. (b) Estimate the area by rounding each length to 1 significant figure, and comment on how close your estimate is.

Show worked answer →

(a) Area $= 24.6 \times 13.8 = 339.48\ \text{cm}^2$ . To 3 significant figures this is $339\ \text{cm}^2$ .

(b) Rounding each length to 1 significant figure: $24.6 \approx 20$ and $13.8 \approx 10$ , so the estimate is $20 \times 10 = 200\ \text{cm}^2$ .

The estimate of $200\ \text{cm}^2$ is much smaller than the true $339\ \text{cm}^2$ because both lengths were rounded down heavily. A 1 significant figure estimate gives only a rough check of the order of magnitude.

Markers reward the exact product, correct rounding to 3 significant figures, a valid estimate from 1 significant figure values, and a sensible comment on accuracy.