Integer Division – Dividing Positive and Negative Numbers
Just as with multiplication, dividing integers requires you to determine the sign of the answer separately from the magnitude.
The Sign Rules
| Calculation | Rule | Result sign |
|---|---|---|
| (+) ÷ (+) | Positive ÷ Positive | Positive |
| (−) ÷ (−) | Negative ÷ Negative | Positive |
| (+) ÷ (−) | Positive ÷ Negative | Negative |
| (−) ÷ (+) | Negative ÷ Positive | Negative |
Memory aid: Same signs → positive quotient. Different signs → negative quotient.
Worked Examples
Examples
(+24) ÷ (+6) = +4
(−24) ÷ (−6) = +4
(+24) ÷ (−6) = −4
(−24) ÷ (+6) = −4
Checking with Multiplication
Always verify: quotient × divisor = dividend.
(−4) × (−6) = +24 ✓ (checks (−24) ÷ (−6) = +4)
Key Takeaways
- Same signs → positive quotient.
- Different signs → negative quotient.
- The magnitude is found by dividing the absolute values.
- Division rules mirror multiplication rules exactly.
Practice Questions
- Calculate (+35) ÷ (+7).
- Calculate (−48) ÷ (−8).
- Calculate (−54) ÷ (+9).
- Calculate (+72) ÷ (−12).
- A submarine descends at a rate of 15 m every minute. If it is at −90 m, how many minutes did the descent take?