Represent the rational numbers 23, −54 and 112 on a single number line.
Step-by-step solution
Idea: Find the two integers each number lies between, divide that unit gap into as many equal parts as the denominator, and count parts from the nearer integer.
- 23 lies between 0 and 1: divide 0 to 1 into 3 equal parts and mark the 2nd point from 0.1 mark
- 112 lies between 1 and 2: divide 1 to 2 into 2 equal parts and mark the middle point.1 mark
- −54 = −114 lies between −2 and −1: divide −1 to −2 into 4 equal parts and mark the 1st point to the left of −1. All three are on the same line (see the diagram).1 mark
Check: Decimals: −1.25, 0.667, 1.5 lie in the stated gaps ✓.
Answer to write in the exam
23: divide 0 to 1 into 3 equal parts, mark 2nd point
112: divide 1 to 2 into 2 equal parts, mark midpoint
−54 = −114: divide −1 to −2 into 4 equal parts, mark 1st point left of −1
∴ The three numbers are marked on one number line (order: −54 < 23 < 112).
Common mistakes that cost marks
- Marking 112 at 12 by ignoring the whole-number part.
- Placing −54 to the right of −1 (between −1 and 0).
- Using a different unit length for each number. All points must use the same scale on the single line.
How this can come in the exam
Which of these lies between −1 and 0 on the number line?
- −54
- −45
- 54
- −73
Show answer
(B) −45
−45 = −0.8 is between −1 and 0; −54 = −1.25 and −73 ≈ −2.33 are left of −1.
Represent −25 and 213 on the same number line. Describe your steps.
Show answer
−25: divide 0 to −1 into 5 equal parts and mark the 2nd point to the left of 0 (1 mark). 213: divide 2 to 3 into 3 equal parts and mark the 1st point after 2 (1 mark).Try one yourself
Describe how to mark 34 and −212 on one number line.
Show answer
34: 3rd of 4 equal parts from 0 to 1. −212: midpoint of −2 and −3.
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