Stage 8 - Q1 - 2 marks
A \(3\frac{1}{2}\) m ribbon loses a \(\frac{1}{2}\) m piece. How much remains?
Hint
The fractional parts match.
Stage 8 - Q2 - 2 marks
Four bags each weigh \(1\frac{1}{4}\) kg. Find the total mass.
Hint
Four quarters form one whole.
Stage 8 - Q3 - 2 marks
How many \(\frac{3}{5}\) L portions are in 6 L?
Hint
Multiply by the reciprocal.
Stage 8 - Q4 - 2 marks
Two quiz scores are \(\frac{17}{20}\) and \(\frac{21}{25}\). Which proportion is greater?
Hint
The denominators both divide 100.
Stage 8 - Q5 - 2 marks
A \(9\frac{2}{3}\) m rope is cut into two pieces. One piece is \(4\frac{5}{8}\) m. Find the other.
Hint
Convert both mixed numbers to improper fractions.
Stage 8 - Q6 - 3 marks
Each short lesson lasts \(\frac{2}{3}\) hour. How many complete lessons fit in 5 hours, and how much time remains?
Hint
The number of complete lessons is a whole number.
Stage 8 - Q7 - 3 marks
A rectangle is \(3\frac{3}{4}\) m wide and 8 m long. A strip \(1\frac{1}{4}\) m wide is removed along the full length. Find the remaining area.
Hint
The removed strip has the same length as the rectangle.
Stage 8 - Q8 - 4 marks
A container holds 8 L. It fills nine \(\frac{3}{4}\) L bottles. What fraction of the original liquid remains?
Hint
Find the leftover volume first; then express it as a fraction of 8.
Stage 8 - Q9 - 4 marks
Find the smallest positive whole number of metres that can be cut exactly into both \(\frac{4}{5}\) m pieces and \(\frac{6}{7}\) m pieces.
Hint
Work backwards from the requirement that both piece counts are integers.
Stage 8 - Q10 - 5 marks
Challenge: a tank contains a whole number of litres greater than 5 and less than 20. Filling \(\frac{3}{4}\) L bottles leaves \(\frac{1}{4}\) L. Filling \(\frac{5}{6}\) L bottles instead leaves \(\frac{1}{6}\) L. Find the original volume and both full-bottle counts.
Hint
List the possible whole-number volumes from one remainder condition, then test the other.