Divide integers

Division of integers is understood as the inverse of multiplication: for a nonzero integer divisor $b$ , the quotient $a \div b$ is the number that satisfies $bq=a$ . The quotient is positive when the nonzero integers have the same sign and negative when they have different signs; zero divided by a nonzero integer is zero, while division by zero is undefined, and non-exact results may be represented as rational numbers. This scope excludes arbitrary rational or algebraic divisors and more advanced number-theoretic treatments.

Detailed Explanation: Divide integers

Division is the inverse of multiplication. To find $a \div b$ , look for the number $q$ that makes

bq=a.

For nonzero integers:

Same signs give a positive quotient.
Different signs give a negative quotient.
Divide the absolute values, then apply the sign.

Example

Find

-48 \div 6.

The signs are different: $-48$ is negative and $6$ is positive. Therefore, the quotient will be negative.
Divide the absolute values:

48 \div 6=8.

Apply the negative sign:

-48 \div 6=-8.

Check using multiplication:

6(-8)=-48.

So,

\boxed{-48 \div 6=-8}.

Remember that $0$ divided by any nonzero integer is $0$ , but division by $0$ is undefined.

Learn by doing: Divide integers

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Negative Integer Division

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