Stage 8 - Q1 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
Equal denominators mean equal-sized parts.
Stage 8 - Q2 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
The numerator is the same; compare the part sizes.
Stage 8 - Q3 - 2 marks
Insert \(<\), \(>\) or \(=\).
Hint
Use a denominator divisible by both 10 and 3.
Stage 8 - Q4 - 3 marks
Order from smallest to largest.
Hint
Use a common denominator for all three fractions.
Stage 8 - Q5 - 2 marks
Leila scores 19 out of 25. Omar scores 31 out of 40. Who has the higher proportion?
Hint
The larger raw score is not enough; compare fractions.
Stage 8 - Q6 - 2 marks
Find a fraction strictly between \(\frac{5}{8}\) and \(\frac{2}{3}\).
Hint
A larger common denominator may create space between the numerators.
Stage 8 - Q7 - 2 marks
Without decimal division, compare \(\frac{48}{49}\) and \(\frac{69}{70}\).
Hint
Compare how far each fraction lies below 1.
Stage 8 - Q8 - 2 marks
Find all integers n for which \(\frac{1}{2}<\frac{n}{10}<\frac{4}{5}\).
Hint
The inequalities are strict, so exclude the endpoints.
Stage 8 - Q9 - 4 marks
A pupil says \(\frac{a}{b}<\frac{a+1}{b+1}\) for all positive a and b. Give a counterexample and explain when it fails.
Hint
Try a fraction greater than 1.
Stage 8 - Q10 - 5 marks
Challenge: find all integers n such that \(\frac{3}{7}<\frac{n}{12}<\frac{4}{5}\), and prove there are no others.
Hint
Turn each fraction comparison into a bound on n, then inspect the integers.