Add and subtract integers

Key notes:

🔹 What are Integers?

• Integers are the set of whole numbers and their negatives, including zero.
  👉 Example: { … –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5 … }

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🔹 Addition of Integers

There are two cases when adding integers:

Same Signs

• Add the absolute values.
• Keep the same sign.
  👉 Example:
  (+7) + (+5) = +12
  (–8) + (–6) = –14

Different Signs

• Subtract the smaller absolute value from the larger absolute value.
• Keep the sign of the number with the greater absolute value.
  👉 Example:
  (+9) + (–4) = +5
  (–12) + (+7) = –5

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🔹 Subtraction of Integers

• To subtract an integer, add its opposite.
  👉 Rule:
  a – b = a + (–b)

🔹 Examples:

1. 7 – (–3) = 7 + 3 = 10
2. (–6) – (+4) = (–6) + (–4) = –10
3. (–5) – (–8) = (–5) + (+8) = +3

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🔹 Number Line Method

Integers can also be added and subtracted using a number line:

• Move right for positive integers.
• Move left for negative integers.

Example on Number Line:

(–3) + 5 → Start at –3, move 5 steps right → ends at +2.

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🔹 Key Rules Summary

1. Adding same signs → Add and keep the sign.
2. Adding different signs → Subtract and keep the sign of the larger number.
3. Subtracting integers → Change subtraction into addition of the opposite.

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🔹 Practice Examples

1. (–15) + (–12) = ?
2. (+25) + (–30) = ?
3. (–8) – (+6) = ?
4. (+12) – (–5) = ?
5. (–20) + (+15) = ?

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✅ Answer Key:

1. –27
2. –5
3. –14
4. +17
5. –5

Learn with an example