Directed numbers · Ages 12–13
Comparing directed numbers
Further right is larger; a negative further from 0 is smaller.
How to do it
Method
Further right is larger; a negative further from 0 is smaller
−7 < −2 < 0 < 3
Another way
Think of temperatures
−7°C is colder than −2°C, so −7 < −2
In full
On a number line, further right is larger, so every positive number is more than 0, and 0 is more than every negative number. Between two negatives, further from 0 is smaller: −7 < −2, as −7 is left of −2. Or think of temperatures: −7°C is colder than −2°C, so −7 is smaller. For negative fractions or decimals, make them all decimals first, then do the same: −34 = −0.75, so −34 < −0.5.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
−21 > −18
True or false?
Show the answer and working
Answer: False
Between negatives, nearer 0 is larger. Compare 21 and 18: the negative with the smaller size is the larger number.
Example 2
Between −6 and 11 (not counting those two) there are integers.
Show the answer and working
Answer: 16
6 − 1 negative ones, 11 − 1 positive ones, and 0: 16 in all. Don't forget 0.
Example 3
Which of these numbers is the largest?
- A. −25
- B. −1
- C. −14
- D. −0.7
Choose the right answer
Show the answer and working
Answer: C. −14
As decimals: 14 = 1 ÷ 4 and 25 = 2 ÷ 5; then see which is nearest 0. Among negatives, nearer 0 is larger.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Which of these numbers is the smallest?
- A. −2
- B. 0
- C. −3
- D. 8
Choose the right answer
Answer:
2.Which of these is true?
- A. −7 < −4
- B. 0 < −4
- C. −7 > 2
- D. −7 > −4
Choose the right answer
Answer:
3.Put these numbers in order, smallest first.
- A. 0
- B. −5
- C. 2
- D. −10
Write the letters in the right order
Answer:
4.Which of these numbers is the largest?
- A. −35
- B. −0.9
- C. −14
- D. −1
Choose the right answer
Answer:
5.Between −13 and 15 (not counting those two) there are integers.
Answer:
All the answers
- 1. C. −3
- 2. A. −7 < −4
- 3. D → B → A → C
- 4. C. −14
- 5. 27
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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