Signed numbers are positive and negative numbers, and the order of operations is the agreed sequence for working out an expression. Most lost marks here come from small habits, not from hard ideas.
How the four skills connect
- Adding and subtracting negative numbers sets up the number line picture.
- Multiplying and dividing signed numbers adds the sign rules for products and quotients.
- Using brackets and operation order combines both inside longer expressions.
- Checking a numerical result with estimation catches slips before you submit.
The order is a dependency chain. Bracket work fails if the sign rules underneath it are shaky.
One slip, three lines later
A worked example from Physics: a ball’s velocity changes from 8 m/s to −2 m/s in 5 s. The change in velocity is −2 − 8 = −10 m/s, so the acceleration is −10 ÷ 5 = −2 m/s².
A student who writes −2 − 8 = −6 gets acceleration −1.2 m/s². The method is perfect and the answer is wrong, because the sign rule failed at line one.
Who should start where
If you get different answers when you redo the same subtraction, begin with the first page. If single-step arithmetic is fine but long expressions go wrong, jump to brackets and operation order.
Students who are not sure can use the prerequisite gap finder to see which skill needs attention. These skills feed directly into algebra readiness, and SPM Mathematics tuition is available for one-to-one practice with working checked live.
A quick self-test before you begin
Try three questions without a calculator: −9 + 4, (−6) × (−2) and 10 − 2 × 3. The answers are −5, 12 and 4.
If any of them differs from yours, open the page for that skill first. Write your own line of working for each before you compare, since the slip is usually visible in how you wrote the line, not only in the answer.