Operations with Integers

Adding Integers

Same signs: Add absolute values, keep the sign. $5 + 3 = 8 \qquad (-5) + (-3) = -8$

Different signs: Subtract absolute values, keep the sign of the larger absolute value. $5 + (-3) = 2 \qquad (-5) + 3 = -2$

Subtracting Integers

Change to addition: Add the opposite of the second number. $a - b = a + (-b)$

Examples: $7 - 10 = 7 + (-10) = -3$ $-4 - 3 = -4 + (-3) = -7$ $-2 - (-6) = -2 + 6 = 4$

Multiplying Integers

| Signs | Result | |-------|--------| | $(+)(+)$ | Positive | | $(-)(-)$ | Positive | | $(+)(-)$ | Negative | | $(-)(+)$ | Negative |

Same signs → positive, different signs → negative

$(-3)(-4) = 12 \qquad (-3)(4) = -12$

Dividing Integers

Same rules as multiplication: $(-12) \div (-3) = 4 \qquad (-12) \div 3 = -4$

Order of Operations with Integers

Follow PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

$-3 + 4 \times (-2) = -3 + (-8) = -11$

Tip: "Two negatives make a positive" only applies to multiplication and division, NOT addition!