Directed numbers · Ages 12–13
Dividing directed numbers
Same signs positive, different negative; never divide by 0.
How to do it
Method
Same signs positive, different negative; never divide by 0
(−12) ÷ 3 = −4
Another way
Think backwards with times
(−4) × 3 = −12
In full
The sign rule is the same as for multiplying: same signs divide to a positive, different signs to a negative, (−12) ÷ (−3) = 4 and (−12) ÷ 3 = −4. Or think backwards: (−12) ÷ 3 asks what times 3 makes −12, and that is −4. Dividing by a fraction is multiplying by its reciprocal: (−6) ÷ (−23) = (−6) × (−32) = 9. 0 divided by any non-zero number is 0, but you can never divide by 0.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The result of (−54) ÷ (+6) is positive.
True or false?
Show the answer and working
Answer: False
Division follows the same sign rule as multiplication: same signs positive, different signs negative.
Example 2
120 ÷ (+3) ÷ (+5): first 120 ÷ (+3) = ; dividing by (+5) then gives .
Fill in each blank
Show the answer and working
Answer: 40, 8
Left to right, checking the signs at each step: 120 ÷ (+3) = 40, and 40 ÷ (+5) = 8.
Example 3
(−15) ÷ (−35) =
Show the answer and working
Answer: 25
Dividing by a fraction is multiplying by its reciprocal: 15 × 53. Same signs give a positive, different signs a negative: 25.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.(+66) ÷ (−11) =
Answer:
2.(−30) ÷ (−15) =
Answer:
3.Which of these has no meaning (can't be worked out)?
- A. (−24) ÷ (−24)
- B. 0 ÷ (−24)
- C. (−24) ÷ 0
- D. 24 ÷ (−1)
Choose the right answer
Answer:
4.72 ÷ (+2) ÷ (+4): first 72 ÷ (+2) = ; dividing by (+4) then gives .
Fill in each blank
Answer:
5.(+23) ÷ (+5) =
Answer in simplest form
Answer:
All the answers
- 1. −6
- 2. 2
- 3. C. (−24) ÷ 0
- 4. 36, 9
- 5. 215
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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