Directed numbers · Ages 12–13
Positive and negative numbers
Right of 0 is positive, left is negative; 0 is neither.
How to do it
Method
Right of 0 is positive, left is negative; 0 is neither
−3 is 3 steps left of 0; −(−3) = 3
Another way
Think of a thermometer
−3 is 3 degrees below zero
In full
Quantities in opposite directions can be told apart by + and −: 5 m east is +5, 5 m west is −5; $300 paid in is +300, $300 taken out is −300. Numbers above 0 are positive, numbers below 0 negative, and 0 is neither. On a number line, positives are right of 0 and negatives left of it: −3 is 3 steps left of 0. Or stand the line up as a thermometer: above 0°C is positive, below zero is negative. 3 and −3 are equally far from 0; they are opposites, so −(−3) = 3.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Walking 40 m east is written +40 m. How should walking 90 m west be written?
- A. −40 m
- B. −90 m
- C. +90 m
- D. +40 m
Choose the right answer
Show the answer and working
Answer: B. −90 m
Opposite directions take opposite signs: east is positive, so west is negative: −90 m.
Example 2
−(−37) =
Show the answer and working
Answer: 37
The minus outside the bracket means the opposite: the opposite of −37 is 37, flipped across 0 on the number line.
Example 3
Each step on this number line is 2. What number is the arrow pointing to?
Show the answer and working
Answer: 8
The arrow is 4 steps from 0. 4 only counts the steps; each is 2, so multiply: 4 × 2. Then see which side of 0 it is on: 8.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.What number is the arrow on the number line pointing to?
Answer:
2.Each step on this number line is 10. What number is the arrow pointing to?
Answer:
3.−(+24) =
Answer:
4.Which of these numbers is furthest from 0?
- A. −15
- B. 6
- C. 0
- D. −8
Choose the right answer
Answer:
5.Each step on this number line is 5. What is the opposite of the number the arrow points to?
Answer:
All the answers
- 1. 4
- 2. −30
- 3. −24
- 4. A. −15
- 5. 10
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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