signed-number arithmetic
Picture a thermometer or a bank account. A positive number is money in or temperature above zero; a negative number is debt or cold below zero. Signed-number arithmetic is the set of rules for adding, subtracting, multiplying, and dividing these positive and negative numbers consistently, so that gains and losses combine the way intuition expects.
For addition, same signs add and keep the sign (−3 + −5 = −8), while opposite signs find the difference of their sizes and take the sign of the larger size (−7 + 4 = −3). Subtracting a number is the same as adding its opposite: 5 − (−2) = 5 + 2 = 7. On a number line, adding a positive moves right and adding a negative moves left.
For multiplication and division, the rule is about signs only: like signs give a positive result, unlike signs give a negative result. So (−4)(−3) = 12 and (−4)(3) = −12. Two negatives making a positive can feel strange; one honest way to see it is that multiplying by −1 reverses direction, and reversing twice returns you to the start.
Compute −6 + 10 − (−4) × 2. Multiply first: (−4) × 2 = −8, so the expression is −6 + 10 − (−8) = −6 + 10 + 8 = 12.
Subtracting a negative becomes adding a positive; signs follow the like/unlike rule.
A subtle point: −3^2 is not 9. Without parentheses the exponent binds tighter than the negative sign, so −3^2 = −(3^2) = −9, while (−3)^2 = 9. Order of operations governs the sign here.