Rational Numbers • Topic 1 of 1

Adding & Subtracting Positive and Negative Integers

Integers are whole numbers that can be positive (+), negative (-), or zero. Think of a number line as your main tool for visualizing integer operations.

Rules for addition:

Same sign: add absolute values and keep the sign. Example: (-3) + (-4) = -7
Different signs: subtract absolute values and keep the sign of the number with the larger absolute value. Example: (-8) + (+3) = -5

Rule for subtraction: Subtracting a number is the same as adding its opposite.

Example: 5 - (-3) = 5 + 3 = 8

Rule	Example	Result
Positive + Positive	4 + 5	+9
Negative + Negative	(-4) + (-5)	-9
Different signs	(-8) + 3	-5
Subtraction rule	5 - (-3)	8

NUMBER LINE: (-5) + (+2)

Start at -5, move 2 steps right --> -3

<--|--|--|--|--|--|--|--|-->
  -5 -4 -3 -2 -1  0  1  2
   ^        ^
  Start    End

KEY RULES SUMMARY:
  Same signs   : add values, keep sign
  Different signs: subtract values, use bigger sign
  a - b        : same as a + (-b)

Solved Examples

Worked Example

A scuba diver is at -12 feet. She rises 7 feet. Where is she now?

Solution-12 + 7 = -5 feet (still below sea level)

Worked Example

The temperature at 6 AM was -8 degrees C. By noon it rose 15 degrees C. What is the noon temperature?

Solution-8 + 15 = +7 degrees C

Worked Example

A bank account has -$20 (overdraft). You deposit $50. What is the new balance?

Solution-20 + 50 = +$30

Key Points

Positive + Positive = Positive
Negative + Negative = Negative (add absolute values)
Positive + Negative = sign of bigger absolute value
To subtract: change minus to plus, flip the sign of the second number

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$(-3)+(-5)=$

Explanation: Same sign: add and keep the sign.

Q2.$(-6)+2=$

Explanation: $-6+2=-4$.

Q3.$5-(-3)=$

Explanation: Subtracting a negative adds.

Q4.$(-7)+7=$

Explanation: Additive inverses.

Practice more MCQs → 📝 Assignment · 35 marks