The numbers work just like always — the only new thing is the sign. Learn the two sign rules once, and multiplying and dividing positive and negative integers becomes automatic.
To multiply or divide integers, first do the math with the plain numbers. Then decide the sign using one simple idea: same signs make a positive, different signs make a negative.
"Same signs, positive. Different signs, negative." This one sentence covers both multiplying and dividing.
Multiply the numbers as usual, then attach the sign from the rule.
4 × 3 = 12, and the signs are different, so the answer is negative.
5 × 2 = 10, and the signs are the same, so the answer is positive.
Ignore the signs for a moment and multiply the plain values.
Same signs → positive. Different signs → negative.
Division follows the exact same sign rule. Writing the division as a fraction makes it easy to see: divide the numbers, then set the sign.
12 ÷ 3 = 4, signs are different → negative.
20 ÷ 4 = 5, signs are the same → positive.
Watch the pattern as the first factor drops by one each time. Every product jumps up by 2 — so continuing the pattern has to make the negatives turn positive:
Just count the negative signs. An even number of negatives gives a positive result; an odd number gives a negative one.
Do the numbers, then set the sign. Answers can be negative.