Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Directed Numbers — adding, subtracting, multiplying and dividing negatives — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Directed Numbers in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Directed Numbers revision-guide angle, while Tutopiya’s Directed Numbers subtopic page owns the learning resource and the free Directed Numbers quiz owns the practice.

Directed Numbers underpin almost every other topic in Cambridge IGCSE Mathematics (0580/0607). Temperature drops, bank balances, elevations below sea level and vector components all rely on confident work with positives and negatives. This guide explains exactly what Directed Numbers covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Directed numbers include positive and negative values; the sign tells you direction on a number line.
• Subtracting a negative is the same as adding: 5 − (−3) = 8.
• Same signs → positive product/quotient; different signs → negative.
• Always apply BIDMAS — brackets before multiplication when negatives are involved.

What are Directed Numbers in Cambridge IGCSE Maths?

Directed Numbers are positive and negative numbers used to represent quantities with direction — above or below zero, profit or loss, gain or decrease. In Cambridge IGCSE Mathematics the subtopic covers ordering negatives, the four operations with directed numbers, and interpreting real contexts on a number line. Examiners test it with short calculations and applied word problems.

You can read the full explanation, worked examples and notes on Tutopiya’s Directed Numbers subtopic page before you attempt questions.

The core ideas you must master

These five ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Number line	Negatives left of zero, positives right	”Write these in order of size”
Adding negatives	Move left on the number line	”Work out −4 + (−7)“
Subtracting negatives	Add the opposite: a − (−b) = a + b	”Calculate 6 − (−5)“
Multiplying signs	Same → +; different → −	“Work out (−3) × (−8)“
Dividing signs	Same rule as multiplication	”Find (−24) ÷ 6”

How to calculate with directed numbers — step by step

The safest approach is to reduce every question to a single signed number using clear rules.

1. Handle brackets first (BIDMAS). Example: 4 − (−2) = 4 + 2 = 6.
2. For multiplication/division, count the negative signs. An even number of negatives → positive; odd → negative. (−3) × (−4) × (−2) = −24.
3. For addition/subtraction, use a number line or rewrite subtraction as adding the opposite.
4. Check the sign before you write the final answer — most slips are sign errors, not arithmetic errors.

Once you have worked through a few, test yourself with the free Directed Numbers quiz — it tells you fast whether the method has actually stuck.

Addition vs subtraction with negatives: which rule applies?

Students lose marks by treating every negative calculation the same way. Match the operation to the rule.

Operation	Rule	Example
a − (−b)	Add: a + b	7 − (−3) = 10
a + (−b)	Subtract: a − b	7 + (−3) = 4
(−a) + (−b)	Add magnitudes, keep negative	(−5) + (−4) = −9
(−a) × (−b)	Positive result	(−6) × (−2) = 12
(−a) × b	Negative result	(−6) × 2 = −12

Directed Numbers in past-paper wording: command words that matter

Most lost marks come from misreading the command word or the context. Cambridge reuses the same phrasing across papers.

Command word / phrase	What the question wants	Typical stem
Work out / Calculate	A numerical answer with method	”Work out −8 + 15.”
Write down	State the answer directly	”Write down the value of (−3)².”
Find the difference between	Subtract (order may matter)	“Find the difference between −5 °C and 3 °C.”
Write these numbers in order of size	Ascending or descending	”Write −4, 2, −7, 0 in order of size.”
Show that	Prove a given result	”Show that (−2) × (−5) = 10.”
Evaluate	Calculate a numerical expression	”Evaluate 12 ÷ (−3) − (−4).”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the maths — is what full marks reward.

1. “Work out −6 − (−9).” Rewrite: −6 + 9 = 3. Reward: correct conversion of subtraction, then answer.
2. “The temperature at midnight was −8 °C. By noon it had risen by 11 °C. Work out the temperature at noon.” −8 + 11 = 3 °C. Reward: correct operation chosen from context.
3. “Write −3, 5, −1, 0 in order of size, starting with the smallest.” −3, −1, 0, 5. Reward: all four values in correct order.

When you can recognise the wording instantly, work the full set on the Number topical past-paper questions and the Directed Numbers quiz to lock the method in.

How Directed Numbers connects to the rest of Number

Directed numbers link to Set Language and Absolute Value, because |x| measures distance regardless of sign. They are essential for Fractions, Decimals and Percentages when finding increases and decreases. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Thinking −3² = 9 — it is −(3²) = −9; use brackets: (−3)² = 9.
• Forgetting that subtracting a negative means adding.
• Misordering negatives: −5 < −2 because −5 is further left on the number line.
• Ignoring BIDMAS when several operations appear in one line.

When you need more support

If negative-number calculations keep tripping you up, work through the Set Language and Absolute Value quiz and the Number topical past-paper questions to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Are Directed Numbers hard in Cambridge IGCSE Maths? No — the rules are fixed. The challenge is applying sign rules consistently, especially with brackets and BIDMAS.

Why is subtracting a negative the same as adding? Because moving left by a negative amount is the same as moving right. On a number line, 5 − (−3) means start at 5 and move 3 to the right → 8.

Is −4 bigger than −2? No. −4 < −2 because −4 is further left on the number line. The more negative value is smaller.

How do I revise Directed Numbers effectively? Read the subtopic notes, practise mixed-operation questions by hand, then take the Directed Numbers quiz to check your method.

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