∑∫ax²+bx+c=0π√x

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By MathPal Editorial Team·Published Apr 10, 2026·Updated Apr 14, 2026

Grade: 6-7 | Topic: Arithmetic

What You Will Learn

By the end of this page you will be able to add any two integers -- whether both are positive, both are negative, or one of each -- using clear sign rules. You will also master subtracting integers by converting every subtraction into an addition problem, and you will feel confident applying these skills to multi-step calculations.

Theory

Why integer addition needs special rules

When you first learned addition, every number was positive. Adding 3 + 5 just meant "move 5 steps to the right on a number line." Negative numbers add a new direction -- moving to the left. That is why we need rules that account for the signs of the numbers.

Rule 1 -- Adding integers with the same sign

When both numbers have the same sign, add their absolute values and keep the common sign.

Same signs: (+a) + (+b) = +(a+b)

Same signs: (−a) + (−b) = −(a+b)

Example: (−7) + (−5) = −(7+5) = −12

Rule 2 -- Adding integers with different signs

When the signs are different, subtract the smaller absolute value from the larger one, then take the sign of the number whose absolute value is larger.

Example: (−9) + 4 = −(9−4) = −5

Example: (−3) + 10 = +(10−3) = 7

Rule 3 -- Subtracting integers (add the opposite)

Every subtraction problem can be rewritten as an addition problem. Change the subtraction sign to addition and flip the sign of the number being subtracted:

a − b = a + (−b)
a − (−b) = a + (+b) = a + b

Quick reference table

Number line approach

You can always verify on a number line:

• Adding a positive number: move right.
• Adding a negative number: move left.
• Subtracting is the same as adding the opposite direction.

Starting at −2 and adding +5 means moving 5 steps right, landing on 3: (−2) + 5 = 3.

Worked Examples

Example 1: Adding two negative integers (easy)

Problem: Calculate (−12) + (−8).

Step 1: Both signs are negative (same sign), so add the absolute values. 12 + 8 = 20.

Step 2: Keep the common sign (negative).

Answer: (−12) + (−8) = −20.

Example 2: Adding integers with different signs (easy)

Problem: Calculate (−15) + 9.

Step 1: The signs are different, so subtract the smaller absolute value from the larger one. 15 − 9 = 6.

Step 2: The larger absolute value belongs to −15 (negative), so the result is negative.

Answer: (−15) + 9 = −6.

Example 3: Subtracting a positive integer (medium)

Problem: Calculate 4 − 13.

Step 1: Rewrite as addition. 4 − 13 = 4 + (−13).

Step 2: Different signs -- subtract absolute values. 13 − 4 = 9.

Step 3: The larger absolute value belongs to −13 (negative), so the result is negative.

Answer: 4 − 13 = −9.

Common Mistakes

Mistake 1: Forgetting to flip the sign when subtracting a negative

❌ 8 − (−5) = 8 − 5 = 3

✅ 8 − (−5) = 8 + 5 = 13

Mistake 2: Applying multiplication sign rules to addition

❌ (−4) + (−6) = +10

✅ (−4) + (−6) = −10

Mistake 3: Losing track of signs in multi-step problems

❌ Solving 5 − 8 + 3 − (−2) left-to-right without rewriting:
5 − 8 = −3, −3 + 3 = 0, 0 − (−2) ... confusion

✅ Rewrite all subtractions first: 5 + (−8) + 3 + 2. Group: positives = 10, negatives = −8. Total = 2.

Practice Problems

Try these on your own before checking the answers:

1. (−9) + (−7)
2. (−11) + 18
3. 15 − 23
4. (−4) − (−12)
5. (−6) + 10 − (−3) − 8

Summary

• Same signs: add absolute values, keep the common sign.
• Different signs: subtract absolute values, take the sign of the number with the larger absolute value.
• Subtraction rule: always rewrite a − b as a + (−b) before computing.
• Double negative: a − (−b) = a + b -- subtracting a negative is the same as adding.
• For multi-step problems, rewrite all subtractions as additions first, then group positives and negatives separately.