A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Division of integers follows the same sign rules as multiplication: dividing two numbers with the same sign gives a positive quotient, and dividing two numbers with different signs gives a negative quotient. This is because division is the inverse of multiplication — if (−3) × (−4) = 12, then 12 ÷ (−4) = −3. Division by zero remains undefined. Integer division is heavily used in solving equations, working with rational expressions, and computing slopes.
Connect explicitly to multiplication: "dividing is asking what number times the divisor gives the dividend." Show that the sign rules must match multiplication's sign rules for consistency. Practice alongside multiplication so students see them as inverse operations. Include problems with zero as the dividend (result is 0) and as the divisor (undefined).
You already know how to multiply integers, including the sign rules: positive × positive = positive, negative × negative = positive, positive × negative = negative. Division inherits exactly these same rules — and the reason is simple. Division is the inverse of multiplication. If you want to know what 12 ÷ (−4) equals, you are asking: "what number, when multiplied by −4, gives 12?" The answer is −3, because (−3) × (−4) = 12. The sign rules for division are not separate facts to memorize — they are forced by consistency with multiplication.
Let's trace through each case. Dividing two positives gives a positive: 15 ÷ 3 = 5, because 5 × 3 = 15. Dividing a negative by a positive (or positive by negative) gives a negative: (−15) ÷ 3 = −5, because (−5) × 3 = −15. Dividing a negative by a negative gives a positive: (−15) ÷ (−3) = 5, because 5 × (−3) = −15. The shortcut: same signs → positive quotient, different signs → negative quotient. This matches multiplication exactly.
Division by zero requires special attention. You cannot divide by zero because there is no number satisfying ? × 0 = 5 — anything times zero is zero, never 5. Division *of* zero is fine: 0 ÷ 5 = 0, because 0 × 5 = 0. These two cases — zero as dividend versus zero as divisor — look superficially similar but are completely different. The inverse-of-multiplication perspective makes them easy to distinguish: ask "what times the divisor gives the dividend?" Zero times anything is zero, so 0 ÷ (any nonzero) = 0. But nothing times zero gives a nonzero number, so (nonzero) ÷ 0 is undefined.