Find three distinct rational numbers that lie strictly between −12 and 14.
Answer: Write −12 = −48 and 14 = 28. Three numbers between them: −38, 0, 18 (others such as −14 or −18 are also correct).
Step-by-step solution
Idea: Give both numbers the same denominator, large enough that several whole-number numerators lie strictly between the two numerators.
- Common denominator 4: −24 and 14. Only −1 and 0 lie between −2 and 1 — not enough room, so use denominator 8.½ mark
- −12 = −48 and 14 = 28. Numerators strictly between −4 and 2: −3, −2, −1, 0, 1.½ mark
- Choose any three: −38, 08 = 0 and 18.1 mark
−3/8, 0 and 1/8 (any three of −3/8, −1/4, −1/8, 0, 1/8 are correct).
Check: Decimals: −0.5 < −0.375 < 0 < 0.125 < 0.25 ✓.
Answer to write in the exam
−12 = −48, 14 = 28
−48 < −38 < 08 < 18 < 28
∴ Three rational numbers: −38, 0, 18
Common mistakes that cost marks
- Picking numbers that are not strictly between, such as −12 itself or 14 itself.
- Forgetting that 0 lies between a negative and a positive number; it is a valid choice.
- Writing −12 = −28 (wrong equivalent fraction).
How this can come in the exam
MCQ (1 mark)
Which number lies between −13 and 16?
- −12
- 15
- −112
- 13
Show answer
(C) −112
−412 < −112 < 212.
Short answer (2 marks)
Find four rational numbers between −23 and −13.
Show answer
Use denominator 15: −1015 and −515 (1 mark). Between: −915, −815, −715, −615 (1 mark).Try one yourself
Find three rational numbers between −34 and −12.
Show answer
−68 and −48 → use 16ths: −1116, −58, −916.
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