Integer addition and subtraction rules

Key Notes:

1. Understanding Integers:

  • Integers include all positive whole numbers, negative whole numbers, and zero.
  • Example: …,-3, -2, -1, 0, 1, 2, 3,…

2. Addition of Integers:

  • Same Signs (Positive + Positive or Negative + Negative):
    • Add the absolute values of the integers.
    • Keep the sign of the integers.
    • Example:
      • (+5) + (+3) = +8
      • (-4) + (-6) = -10
  • Different Signs (Positive + Negative or Negative + Positive):
    • Subtract the smaller absolute value from the larger absolute value.
    • The sign of the result is the same as the sign of the integer with the larger absolute value.
    • Example:
      • (+7) + (-4) = +3
      • (-5) + (+8) = +3

3. Subtraction of Integers:

  • (-3) – (+2) = (-3) + (-2) = -5

Change the Subtraction to Addition:

Subtraction of an integer is the same as adding its opposite.

Formula: a−b=a+(−b)a – b = a + (-b)a−b=a+(−b)

Example:

  • 6−3=6+(−3)=3
  • −8−5=−8+(−5)=−13

Same Signs (Positive – Positive or Negative – Negative):

Follow the same rules as addition, but with subtraction.

Example:

  • (+10) – (+4) = +6
  • (-7) – (-3) = -4 (since subtracting a negative is like adding its positive)

Different Signs (Positive – Negative or Negative – Positive):

Change subtraction to addition by adding the opposite of the second integer.

Example:

  • (+4) – (-3) = (+4) + (+3) = +7
  • (-3) – (+2) = (-3) + (-2) = -5

Learn with an example

➡️ Is 83 − 79 positive or negative?

  • positive
  • negative

Since you are subtracting a smaller positive number, 79, from a larger positive number, 83, the result remains positive.

You can check your answer by doing the maths.

83 − 79 = 4

As you can see, the result is positive.

➡️ Is -1 + 41 positive or negative?

  • positive
  • negative

When you add a negative number, –1, and a positive number, 41, the result has the same sign as the number with the larger magnitude.

The magnitude of -1 is 1.

The magnitude of 41 is 41.

Since 41 has a larger magnitude and 41 is positive, the result is positive.

You can check your answer by doing the maths.

-1 + 41 = 40

As you can see, the result is positive.

➡️ Is -8 − (-91) positive or negative?

  • positive
  • negative

Since you are subtracting a negative number, add a positive number instead:

-8 −( -91) = -8 + 91

Now you have a negative number, –8, and a positive number, 91. The result has the same sign as the number with the larger magnitude.

The magnitude of -8 is 8.

The magnitude of 91 is 91.

Since 91 has a larger magnitude and 91 is positive, the result is positive.

You can check your answer by doing the maths.

-8 − (-91) = 83

As you can see, the result is positive.

Try some practice problems!