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Sources & Methodology
Integer arithmetic rules verified against Khan Academy 6th-grade math curriculum and NCTM Number and Operations standards.
Khan Academy — Adding Integers with Different Signs
Curriculum-standard explanation of integer addition sign rules used as reference for step-by-step output
National Council of Teachers of Mathematics (NCTM)
Standards for integer operations confirming sign rules and number line methodology
Addition methodology: Same signs → add absolute values, keep the sign. Different signs → subtract smaller absolute value from larger, keep sign of larger. Subtraction methodology: a − b = a + (−b). Convert to addition then apply addition rules. Result classified by sign and magnitude.
⏱ Last reviewed: April 2026
How to Add and Subtract Integers
Integers are all whole numbers including zero and their negatives: …−3, −2, −1, 0, 1, 2, 3… Adding and subtracting them follows specific sign rules that differ from natural numbers. Mastering these rules is foundational for algebra, accounting, temperature changes, and any calculation involving gains and losses.
Rules for Adding Integers
Same signs: add absolute values, keep the sign
(+5) + (+3) = +8 (both positive: add, keep positive)
(−5) + (−3) = −8 (both negative: add, keep negative)
(−5) + (−3) = −8 (both negative: add, keep negative)
Different signs: subtract absolute values, keep sign of larger
5 + (−8): |8| > |5|, so 8 − 5 = 3, sign of −8 wins → −3
(−3) + 7: |7| > |3|, so 7 − 3 = 4, sign of +7 wins → +4
(−3) + 7: |7| > |3|, so 7 − 3 = 4, sign of +7 wins → +4
Rules for Subtracting Integers
a − b = a + (−b) — subtracting = adding the opposite
7 − (−4) = 7 + 4 = 11 (minus a negative = plus a positive)
(−6) − (−2) = (−6) + 2 = −4
5 − 8 = 5 + (−8) = −3
(−6) − (−2) = (−6) + 2 = −4
5 − 8 = 5 + (−8) = −3
Integer Operations Reference Table
| Expression | Rewritten | Result | Rule Applied |
|---|---|---|---|
| (−4) + (−3) | −(4+3) | −7 | Same signs: add, keep negative |
| 5 + (−8) | −(8−5) | −3 | Diff signs: |8|>|5|, keep negative |
| (−3) + 7 | +(7−3) | +4 | Diff signs: |7|>|3|, keep positive |
| 7 − (−4) | 7 + 4 | +11 | Subtract negative = add positive |
| (−6) − (−2) | (−6) + 2 | −4 | Convert subtraction, diff signs |
| 0 − (−5) | 0 + 5 | +5 | Subtract negative = add positive |
| (−10) + 10 | −(10−10) | 0 | Opposites cancel to zero |
Integer Operations on a Number Line
A number line makes integer arithmetic visual. Start at the first integer. For addition: move right for positive numbers, move left for negative numbers. For subtraction: convert to addition of the opposite first, then apply the same movement rules. Example: 4 − 7 = 4 + (−7) → start at 4, move 7 left → land at −3.
Real-World Applications of Integer Operations
Integer arithmetic models many real situations: bank account balance changes (deposits = positive, withdrawals = negative), temperature changes above and below zero, elevation above and below sea level, football yardage gains and losses, and profit/loss accounting. The sign rules ensure calculations work correctly in all these contexts.
💡 Key rule to remember: Subtracting a negative is ALWAYS the same as adding a positive. "Minus a minus equals a plus." So a − (−b) = a + b, every time, no exceptions.
Frequently Asked Questions
Add their absolute values and keep the negative sign. Example: (−4) + (−3) = −(4+3) = −7. Both numbers are negative so the sum is always negative and larger in magnitude than either individual number.
Subtract the smaller absolute value from the larger. The answer takes the sign of the number with the larger absolute value. Example: 5 + (−8): |8| > |5|, so 8 − 5 = 3, and since −8 has larger absolute value, the result is −3.
(−5) + 3 = −2. Absolute values are 5 and 3. Since |5| > |3|, subtract: 5 − 3 = 2. Since −5 has the larger absolute value, the result is negative: −2.
Subtracting a negative is the same as adding a positive: a − (−b) = a + b. Example: 5 − (−3) = 5 + 3 = 8. The two negatives (the minus sign and the negative) combine to form a positive.
7 − (−4) = 7 + 4 = 11. Subtracting a negative converts to addition. Two negatives make a positive, so −(−4) = +4.
(−6) − (−2) = (−6) + 2 = −4. Convert subtraction to addition: −(−2) = +2. Now (−6) + 2: since |6| > |2|, subtract: 6 − 2 = 4, keep the negative: −4.
Subtract the smaller absolute value from the larger, then use the sign of the number with the larger absolute value. Example: (−9) + 4: |9| > |4|, subtract 9 − 4 = 5, sign of −9 wins: answer = −5.
(−3) + (−7) = −10. Both integers are negative so add their absolute values: 3 + 7 = 10, and keep the negative sign: −10.
Convert subtraction to addition of the opposite first. Then on a number line, adding a positive moves right and adding a negative moves left. Example: 4 − 7 = 4 + (−7): start at 4, move 7 left, land at −3.
0 − (−5) = 0 + 5 = 5. Subtracting a negative converts to adding a positive. Starting from 0 and adding 5 gives 5.
Adding integers combines two values using sign rules. Subtracting integers is defined as a − b = a + (−b) — you add the opposite. Once subtraction is rewritten as addition, both operations use the same sign rules.
(−10) + 6 = −4. Absolute values are 10 and 6. Since |10| > |6|, subtract: 10 − 6 = 4. Since −10 has the larger absolute value, the result is negative: −4.
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