Directed-number calculations
Objective. Calculate with positive and negative integers using all four operations.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Directed-number calculations combine positive and negative integers using addition, subtraction, multiplication and division. Adding a negative number means moving left on a number line, while subtracting a negative means moving right, so 5 − (−3) = 8. For multiplication and division, two signs the same give a positive answer and two signs different give a negative answer, so (−4) × (−3) = 12 but (−4) × 3 = −12. Always work out the sign of the answer first, then the size of the numbers. A useful check is to picture temperature changes or bank balances to see whether the result should be bigger or smaller.
Worked example
Calculate (−6) + 4 − (−9) using directed-number rules.
- 1Rewrite subtracting a negative as adding: (−6) + 4 + 9
- 2Add the first two terms: (−6) + 4 = −2
- 3Add the result to 9: −2 + 9 = 7
- 4Check by reordering: 4 + 9 − 6 = 7
Answer: 7
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often write −3 − 4 = −1 by subtracting sizes instead of adding the magnitudes, forgetting both numbers move the value further negative; the correct answer is −7. Always rewrite subtraction of a positive as moving further left.
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