Ordering integers on a number line, then the two adding rules and the 'add the opposite' trick for subtracting — with a number-line diagram, exam-style worked examples, a worksheet with memo and a quick quiz.
An integer is a whole number that can be positive, negative or zero: … −3, −2, −1, 0, 1, 2, 3 … If one skill decides how smoothly the rest of high school maths goes, it is working confidently with negative numbers. A single sign slip turns a correct method into a wrong answer, so this is worth mastering properly.
1Ordering and comparing integers
On a number line, values get bigger as you move right and smaller as you move left. That is the whole rule for comparing integers — and it catches learners out with negatives, because −7 is smaller than −2 even though 7 looks like the bigger number.
- 1Ascending means smallest first.Read it as 'left to right on the number line'.
- 2The negatives come first, most negative of all being −8, then −2.−8 is further left than −2, so it is smaller.
- 3Answer: −8, −2, 0, 3, 5.Then 0, then the positives in order.
Very common slip: writing −2 < −8. It is the other way around — −8 < −2, because −8 sits further left. With negatives, the bigger the digit, the smaller the number.
2Adding: same signs
- 1Both signs are negative — the same.So use the same-signs rule.
- 2Add the sizes: 6 + 4 = 10.Ignore the signs for a moment and just add.
- 3Keep the shared sign: −10.Two negatives added give a bigger negative (further left).
3Adding: different signs
- 1Signs differ, so subtract the sizes: 9 − 5 = 4.A positive and a negative partly cancel each other.
- 2The 9 was negative and it is the bigger size, so the answer is negative.The bigger size decides the sign.
- 3Answer: −4.
4Subtracting: add the opposite
This one trick removes nearly all the confusion: every subtraction can be rewritten as an addition. Change the − to a +, flip the sign of the number after it, then use the two adding rules above.
subtracting is the same as adding the opposite
- 1Rewrite: 3 − (−8) = 3 + (+8).Subtracting a negative is adding a positive — two touching minus signs make a plus.
- 2Same signs now, so add: 3 + 8 = 11.
- 3Answer: 11.
- 1Rewrite: (−4) − 7 = (−4) + (−7).Subtracting a positive is adding a negative.
- 2Same signs, add the sizes: 4 + 7 = 11, keep negative.
- 3Answer: −11.
The number-one mistake: reading −(−8) as −8. Two negatives cancel to a positive, so −(−8) = +8. Always pause when you see two signs touching.
5A real-life check: temperature
- 1'Drops by 5' means subtract 5: −3 − 5.Falling temperature moves left on the number line.
- 2Rewrite as adding: −3 + (−5) = −8.Same signs, so add the sizes and keep the negative.
- 3The temperature is −8 °C.Always answer in words with the unit.
Practice exercises
Work each one out, then click to reveal the answer.
- 1Arrange in ascending order: −4, 6, −9, 0, 2
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−9, −4, 0, 2, 6 - 2Fill in < or >: −7 ___ −3
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−7 < −3 (−7 is further left) - 3(−8) + (−5)
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Same signs → 8+5 = 13 → −13 - 4(−12) + 7
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Different signs → 12−7 = 5, bigger is negative → −5 - 515 + (−20)
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Different signs → 20−15 = 5, bigger is negative → −5 - 66 − (−9)
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6 + 9 = 15 - 7(−4) − 7
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−4 + (−7) = −11 - 8(−7) − (−10)
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−7 + 10 = 3 - 9The temperature is −6 °C and rises by 4 °C. What is the new temperature?
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−6 + 4 = −2 °C - 10A submarine at −120 m rises 45 m. What is its new depth?
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−120 + 45 = −75 m
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