Stage 8 - Q1 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
A number farther left on the number line is smaller.
Stage 8 - Q2 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
Every negative number lies below zero.
Stage 8 - Q3 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
Use denominator 8 and keep the minus signs.
Stage 8 - Q4 - 3 marks
Order from smallest to largest.
Hint
Compare their positive magnitudes, then reverse the order.
Stage 8 - Q5 - 2 marks
The temperatures are \(-1\frac{2}{3}\)°C and \(-1.65\)°C. Which is warmer?
Hint
Write enough decimal digits to see the first difference.
Stage 8 - Q6 - 2 marks
Find a fraction strictly between \(\frac{-5}{6}\) and \(\frac{-3}{4}\).
Hint
Equivalent fractions can reveal a numerator between the endpoints.
Stage 8 - Q7 - 2 marks
Find all integers n for which \(-1<\frac{n}{6}<\frac{-1}{3}\).
Hint
The endpoints are excluded.
Stage 8 - Q8 - 2 marks
A pupil orders \(\frac{-7}{9}\), \(\frac{-5}{6}\), \(\frac{-4}{5}\) by their numerators. Correct the order and explain.
Hint
Compare all three with one common denominator.
Stage 8 - Q9 - 4 marks
If \(0<a<b\), compare \(\frac{-1}{a}\) and \(\frac{-1}{b}\). Justify with positive fractions first.
Hint
Apply the reciprocal comparison, then account for the negative sign.
Stage 8 - Q10 - 5 marks
Challenge: find all integer numerators n such that \(\frac{-7}{8}<\frac{n}{12}<\frac{-2}{3}\). Explain why the interval contains exactly those possibilities.
Hint
Find the allowable interval for the numerator before listing integers.