Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Counters are in the ratio 2 red to 3 blue. How many counters are in one group?
Show worked solution
5.
2 In the ratio 2 red to 3 blue there are 3 groups. Write the number of red counters and the number of blue.
Show worked solution
6 red and 9 blue.
3 $18 buys 3 notebooks. How many dollars does one notebook cost?
Show worked solution
6 dollars.
Level 2 · Core
4 Counters are in the ratio 2 red to 3 blue and there are 15 blue. How many red counters are there?
Show worked solution
15 ÷ 3 = 5 groups, so 5 × 2 = 10 red.
5 $40 is shared in the ratio 3 : 5. Write the value of one part, and the larger share.
Show worked solution
One part is $5, so the larger share is 5 × 5 = $25.
6 $18 buys 3 notebooks. How many notebooks can be bought for $42?
Show worked solution
7 notebooks.
Level 3 · Challenge
7 Counters are in the ratio 2 red to 3 blue.1 Every group has 5 counters.
2 If there are 12 red then there are 18 blue.
3 The total number of counters could be 12.
Which statements are correct?
2 If there are 12 red then there are 18 blue.
3 The total number of counters could be 12.
Which statements are correct?
Show worked solution
2 + 3 = 5 a group (1 ✓); 12 red is 6 groups, so 18 blue (2 ✓). 12 is not a multiple of 5, so the total cannot be 12 (3 ✗). 1 and 2.
8 A car travels 240 km on 20 litres of petrol. Write how far it goes on one litre, and how far it would go on 35 litres.
Show worked solution
240 ÷ 20 = 12 km per litre, and 12 × 35 = 420 km.
9 $56 is shared between two people in the ratio 3 : 4. How many dollars does the person with the larger share get?
Show worked solution
$56 ÷ 7 = $8 a part, and 4 × 8 = $32.