Integers

Integers are closed under addition, subtraction and multiplication. Addition and multiplication are commutative and associative, and multiplication is distributive over addition.

The additive identity is 0 (a + 0 = a) and the multiplicative identity is 1 (a × 1 = a). The additive inverse of a is −a, since a + (−a) = 0.

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

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)

Integers describe real situations: a temperature rise is positive and a fall is negative, height above sea level is positive and depth below is negative, and a bank deposit is positive while an overdraft is negative.