Stage 9 - Q1 - 2 marks
Multiply and simplify.
Hint
A factor in any numerator can cancel with a factor in any denominator.
Stage 9 - Q2 - 2 marks
Multiply and simplify.
Hint
A factor in any numerator can cancel with a factor in any denominator.
Stage 9 - Q3 - 2 marks
Multiply and simplify.
Hint
A factor in any numerator can cancel with a factor in any denominator.
Stage 9 - Q4 - 2 marks
Multiply and simplify.
Hint
A factor in any numerator can cancel with a factor in any denominator.
Stage 9 - Q5 - 4 marks
Of 240 badges, two fifths are sold first. Then \(\frac{3}{8}\) of the remainder are sold. Find the number left.
Hint
After the first sale, only three fifths remain.
Stage 9 - Q6 - 4 marks
A walker moves at \(4\frac{1}{2}\) km/h for 75 minutes. Find the distance.
Hint
The time unit must match the speed unit.
Stage 9 - Q7 - 3 marks
Does multiplying \(2\frac{3}{4}\) by an improper fraction always make it strictly larger?
Hint
Distinguish “at least 1” from “greater than 1”.
Stage 9 - Q8 - 4 marks
One third of a stock is sold, then one fifth of the remainder. \(80\) items remain. Find the original stock.
Hint
Work backwards from the fraction retained.
Stage 9 - Q9 - 4 marks
From 168 cards, A takes two sevenths; B takes one third of the remainder. Who takes more, and by how many?
Hint
B’s fraction is not one third of the original.
Stage 9 - Q10 - 5 marks
Challenge: A takes an unknown fraction \(p\) of 72 tokens. B takes \(\frac1{5}\) of what remains. They take equal numbers. Find p, each person’s amount and the number left.
Hint
Express both portions as fractions of the original stock.