Directed numbers · Ages 12–13
Using directed numbers
Choose the positive direction, write the sum, answer in words.
How to do it
Method
Choose the positive direction, write the sum, answer in words
−3°C, falling 4°C: (−3) + (−4) = −7
Another way
Draw an upright number line
From −3, 4 steps down, to −7
In full
First decide which way is positive: up, profit and paying in are positive, so down, loss and taking out are negative. Write the story as a sum, work it out by the rules, then answer in words. It is −3°C and falls another 4°C: (−3) + (−4) = −7, so −7°C. For how far apart two positions are, take the smaller from the larger: 3 − (−7) = 10. Or draw the story on an upright number line and count the steps: the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
It was −7°C at dawn and 24°C at noon. By how much did the temperature rise?
Show the answer and working
Answer: 31°C
24 − (−7) = 24 + 7 = 31. Up to 0°C first, then on to 24°C.
Example 2
A submarine is 60 m below sea level and dives 30 m more. Which sum gives its new position?
- A. 60 − (−30)
- B. (−60) + 30
- C. 60 + (−30)
- D. (−60) + (−30)
Choose the right answer
Show the answer and working
Answer: D. (−60) + (−30)
With sea level 0 and up positive: start at −60, then change by −30: (−60) + (−30).
Example 3
With London as 0, city A is −10 hours and city B +10 hours. How many hours is B's clock ahead of A's?
Show the answer and working
Answer: 20 hours
10 − (−10) = 10 + 10 = 20. They are on either side of 0, so add.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.It was −5°C at dawn and 3°C at noon. By how much did the temperature rise?
Answer:
2.A shop's record over three days is +$250, −$400, −$300. With profit positive, what is its total over the three days, in dollars?
Answer:
3.A submarine is 80 m below sea level and dives 10 m more. Which sum gives its new position?
- A. (−80) + 10
- B. 80 − (−10)
- C. 80 + (−10)
- D. (−80) + (−10)
Choose the right answer
Answer:
4.An account holds $600, and $200 is taken out (it may go overdrawn, written as negative). What is the balance, in dollars?
Answer:
5.A quiz has 12 questions: +1 for right, −2 for wrong. All are answered, 6 wrong. What is the total score?
Answer:
All the answers
- 1. 8°C
- 2. −450 dollars
- 3. D. (−80) + (−10)
- 4. 400 dollars
- 5. −6 points
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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