Dividing Signed Numbers

When 18 is divided by 9 the result is 2. Here 18 is the dividend, 9 the divisor, and 2 the quotient, and they're connected by \text{quotient} \times \text{divisor} = \text{dividend}. We know 2 is right because 2 \times 9 = 18. That same test tells us the sign of any quotient:

• +18 \div +9 = +2, because +2 \cdot +9 = +18.
• -18 \div +9 = -2, because -2 \cdot +9 = -18.
• +18 \div -9 = -2, because -2 \cdot -9 = +18.
• -18 \div -9 = +2, because +2 \cdot -9 = -18.

Rule. The quotient of two numbers with like signs is positive. The quotient of two numbers with unlike signs is negative.

Never divide by zero

Multiplying by zero always gives zero, in arithmetic and in algebra. But division by zero is always excluded, because it leads to contradictions. For example, 0 \cdot 4 = 0 and 0 \cdot 5 = 0, so 0 \cdot 4 = 0 \cdot 5. If we could divide both sides by zero, we'd get 4 = 5!

Zero divided by a number is fine, though: 0 \div 5 = 0.