Read

Understanding Integer Division

Dividing integers follows the same sign rule as multiplying: divide the numbers first, then check the signs. Matching signs (both positive or both negative) give a positive quotient; different signs give a negative quotient. Negative 20 divided by 4 equals negative 5. Learn why the rule matches multiplication.

The sign rules for dividing integers

Dividing integers follows the exact same sign pattern as multiplying integers: matching signs give a positive quotient, and different signs give a negative quotient. Divide the numbers as if they were positive, then apply the sign rule.

Matching signs give a positive quotient; mixed signs give a negative quotient.

Worked example

For −20 ÷ 4: divide as if both were positive (20 ÷ 4 = 5), then check the signs. One number is negative and one is positive, which is a mixed pair, so the answer is negative: −20 ÷ 4 = −5.

Why the same rule works for both operations

Division is the reverse of multiplication, so if −5 × 4 = −20, then −20 ÷ 4 must equal −5. Because multiplying and dividing undo each other, the sign of the quotient always matches the sign that multiplication would have produced.

Related skills

Once dividing integers feels solid, applying integer operations mixes division with the other operations in multi-step problems.

Related lessons

Basic Math