Integer Rules

When adding integers with the same sign, simply add their absolute values and keep the original sign. For example, $5 + 15 = 20$ (both positive) or $-15 + (-20) = -35$ (both negative).

For adding integers with different signs, subtract the smaller absolute value from the larger one and use the sign of the number with the larger absolute value. For instance, $-5 + 15 = 10$ (keep the positive sign) or $15 + (-20) = -5$ (keep the negative sign).

Subtraction can be tricky, but there's a simple trick: "Keep, Change, Change." Keep the first number, change the subtraction to addition, and change the second number to its opposite. So $-25 - 80$ becomes $-25 + (-80) = -105$.

Remember: For multiplication and division, the sign rule is straightforward - same signs give you a positive answer, different signs give you a negative answer. For example, $-4 \times 5 = -20$ (different signs) and $-14 \times (-18) = 252$ (same signs).

When working with these rules, try to visualize the numbers on a number line to help understand what's happening with the positive and negative values.