Multiplying and Dividing Integers

Multiplication and division of integers follow one clean sign rule:

• Same signs → positive. $(-5)\times(-6) = 30$.
• Different signs → negative. $(-3)\times 4 = -12$.

Division behaves identically: $(-20)\div 4 = -5$ and $(-18)\div(-3) = 6$.

When several numbers are multiplied, just count the negative signs: an even count gives a positive answer, an odd count gives a negative one. For example $(-2)\times(-3)\times(-1)$ has three negatives, so the answer is negative: $-6$.

Exam checkpoint

For multiplication or division, work out the size first and the sign second. Same signs give a positive result; different signs give a negative result. A context can help: a repeated loss is negative, while reversing a loss can be positive. State the sign rule in working when the question has several negatives.

Short worked example. A game removes 4 points in each of 6 penalty rounds: $(-4)\times6=-24$. If a total loss of $-24$ is shared over 6 rounds, $-24\div6=-4$.