Directed numbers · Ages 12–13
Subtracting directed numbers
Taking away a number = adding its opposite.
How to do it
Method
Taking away a number = adding its opposite
5 − (−3) = 5 + 3 = 8
Another way
Look at the distance
From −3 to 5: 8 steps right
In full
Taking away a number is adding its opposite: 5 − (−3) = 5 + 3 = 8, and (−2) − 6 = (−2) + (−6) = −8. Once it is an addition, the addition rules apply. Another way is to look at the distance: a − b is how far it is from b to a, right positive and left negative. From −3 to 5 is 8 steps right, so 5 − (−3) = 8, the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The two dots on the number line are −5 and 2. The distance between them is 2 − (−5). What is it?
Show the answer and working
Answer: 7
From −5 to 0 is 5 steps, from 0 to 2 is 2 steps: 7 in all. The sum 2 − (−5) = 2 + 5 = 7 agrees.
Example 2
(−11) − (−7) − (−6) =
Show the answer and working
Answer: 2
Turn each minus into adding the opposite: (−11) + (+7) + (+6) = 2.
Example 3
Which of these comes to 7?
- A. 14 − 21
- B. 14 − (−21)
- C. (−14) − (−21)
- D. (−14) − 21
Choose the right answer
Show the answer and working
Answer: C. (−14) − (−21)
Make each subtraction add the opposite: (−14) − (−21) = (−14) + 21 = 7.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.(−13) − (−53) =
Answer:
2.−21 − 17 =
Answer:
3.The two dots on the number line are −6 and 9. The distance between them is 9 − (−6). What is it?
Answer:
4.(+56) − (−40) =
Answer:
5.(+17) − (−10) − (+11) =
Answer:
All the answers
- 1. 40
- 2. −38
- 3. 15
- 4. 96
- 5. 16
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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