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Dividing Integers
Because division is the inverse operation of multiplication, every division fact corresponds to a multiplication fact. For example, because . This inverse relationship means the sign rules for dividing integers mirror those for multiplication:
- Same signs → positive quotient: When the dividend and divisor share the same sign, the quotient is positive. For example, so , and so .
- Different signs → negative quotient: When the dividend and divisor have opposite signs, the quotient is negative. For example, so , and so .
Two special cases involve zero:
- Zero divided by any nonzero integer is : For any , . For example, .
- Division by zero is undefined: For any integer , the expression has no defined value, because no number multiplied by can produce a nonzero result.
Because of this inverse relationship, a division answer can always be checked by multiplying the quotient by the divisor to see whether the dividend is recovered.
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