Divide a Signed Total
Find a signed per-interval change and check by multiplication.
Supplied materials
- Paper or a note app.
- Fictional position change: −18 units over 3 equal intervals.
Learn the idea
Division can recover the equal change in each interval from a total change. If the total is negative and the number of intervals is positive, each equal change is negative. Eighteen units down over three intervals gives six units down each time.
Check any quotient by multiplying it by the nonzero divisor. For signed numbers, equal signs in dividend and divisor give a positive quotient; opposite signs give a negative quotient. Division by zero is undefined, so it cannot provide a per-interval rate.
- Write the unknown interval change as c and the check 3c = −18.
- Divide −18 by 3 to find −6 units per interval.
- Check 3 × (−6) = −18, then compute (−24) ÷ (−6).
See the method in action
−18 ÷ 3 = −6 units per interval. Multiplication checks this because 3 × (−6) = −18. Algebraically, (−18) ÷ (−3) = +6 because (−3) × 6 = −18.
Check your reasoning
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See the answer and explanation
4
The two signs match, so the quotient is positive: 24 ÷ 6 = 4. Checking (−6) × 4 = −24 verifies it.
Take it further
Change the divisor to +6. Then (−24) ÷ 6 = −4; 6 × (−4) = −24. The same magnitude now has a negative sign.
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