Stage 8 - Q1 - 2 marks
Write this ratio in its simplest form.
Hint
Find a common factor of every term.
Stage 8 - Q2 - 2 marks
Write this ratio in its simplest form.
Hint
Find a common factor of every term.
Stage 8 - Q3 - 2 marks
Write this ratio in its simplest form.
Hint
Find a common factor of every term.
Stage 8 - Q4 - 2 marks
Find the missing term so the ratios are equivalent.
Hint
Use the multiplier from the first term to the corresponding term.
Stage 8 - Q5 - 2 marks
Which ratio is equivalent to \(4:6\): \(12:18\) or \(16:20\)? Justify your answer.
Hint
Simplify all three ratios before comparing.
Stage 8 - Q6 - 2 marks
The simplest ratio of two positive integers is \(4:7\). Their highest common factor is 9. Find the two integers.
Hint
Multiply both simplest-form terms by the given common factor.
Stage 8 - Q7 - 2 marks
Red : blue counters is \(2:5\). The total is greater than 40 and less than 50. Find every possible total.
Hint
Use the total number of parts to restrict the possible totals.
Stage 8 - Q8 - 2 marks
Three positive integers have simplest ratio \(3:4:5\) and sum 144. Find the integers and check the ratio.
Hint
Compare the sum of the actual numbers with the sum of the ratio terms.
Stage 8 - Q9 - 4 marks
Two positive integers have simplest ratio \(3:5\) and differ by 26. Find them and explain why the answer is unique.
Hint
Write the numbers as three and five times the same unknown.
Stage 8 - Q10 - 5 marks
Red : blue is \(3:4\) and blue : green is \(6:5\). Find red : blue : green in simplest form.
Hint
Match the middle colour before joining the ratios.