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.
15 questions · official format, shuffled order
1 Three eighths of a number is 36. What is five sixths of the same number?
Show worked solution
One eighth is 36 ÷ 3 = 12, so the number is 8 × 12 = 96. One sixth of 96 is 16, and five sixths is 80.
2 Three identical cakes are shared. How much cake is left?
Show worked solution
1⅓ = 8 sixths, ⅚ = 5 sixths, ½ = 3 sixths: 16 sixths eaten out of 18. Two sixths are left, which is 1/3.
3 The line from 0 to 1 is divided into 12 equal parts. Which fraction is not equal to the arrow's position?
Show worked solution
9/12 = 3/4. 6/8, 15/20 and 18/24 all simplify to 3/4 as well. 7/9 does not — it is a little less than 3/4.
4 Which fraction lies between 2/3 and 3/4?
Show worked solution
2/3 ≈ 0.67 and 3/4 = 0.75. 7/10 = 0.7 sits between them. 5/8 = 0.625 and 13/20 = 0.65 are too small; 4/5 = 0.8 is too big.
5 Jo paints 3/8 of a fence on Monday and 1/4 of it on Tuesday. What fraction of the fence is still unpainted?
Show worked solution
1/4 = 2/8, so 3/8 + 2/8 = 5/8 painted. 8/8 − 5/8 = 3/8 unpainted.
6 Six children share four pizzas equally. What fraction of a pizza does each child get?
Show worked solution
4 ÷ 6 = 4/6 = 2/3 of a pizza each. (1 1/2 is pizzas per child the wrong way round: 6 ÷ 4.)
7 P and Q are marked on a number line from 0 to 1 divided into twentieths.1 P is less than a half.
2 Q is more than three fifths.
3 P is one quarter of Q.
Which statements are correct?
2 Q is more than three fifths.
3 P is one quarter of Q.
Which statements are correct?
Show worked solution
P = 6/20 = 3/10, under a half (1 ✓). Q = 15/20 = 3/4, more than 12/20 (2 ✓). A quarter of Q would be 15/80, but P is 24/80 (3 ✗). 1 and 2.
8 A rope is 3 m long. Two fifths of it is cut off, and then one quarter of what remains is cut off. How much rope is left, in centimetres?
Show worked solution
2/5 of 300 = 120, leaving 180. 1/4 of 180 = 45, leaving 135 cm.
9 How many quarters are there in 5 3/4 + 2 1/2 altogether?
Show worked solution
5 3/4 = 23 quarters and 2 1/2 = 10 quarters. 23 + 10 = 33 quarters.
10 Which of these is the largest?
Show worked solution
7/4 = 1.75. Both 1 5/8 and 13/8 are 1.625, and both 1 1/2 and 15/10 are 1.5.
11 In a class of 28, three sevenths are boys. One quarter of the boys wear glasses. How many boys do not wear glasses?
Show worked solution
28 ÷ 7 = 4, so 3/7 is 12 boys. 1/4 of 12 = 3 wear glasses, so 12 − 3 = 9 do not.
12 A tank is five sixths full. Then two thirds of the tank's capacity is pumped out. What fraction of the tank is still full?
Show worked solution
2/3 = 4/6. 5/6 − 4/6 = 1/6.
13 1 5/9 is greater than 1/2.
2 7/15 is greater than 1/2.
3 11/20 is greater than 5/9.
Which statements are correct?
2 7/15 is greater than 1/2.
3 11/20 is greater than 5/9.
Which statements are correct?
Show worked solution
5 > 4.5, so 5/9 > 1/2 (1 ✓). 7 < 7.5, so 7/15 < 1/2 (2 ✗). 11/20 = 0.55 and 5/9 ≈ 0.556, so 11/20 is smaller (3 ✗). 1 only.
14 This sequence goes up by the same amount each time. What is the 10th term?
Show worked solution
Nine steps of 1/4 is 9/4 = 2 1/4. 1/2 + 2 1/4 = 2 3/4.
15 Priya spends two fifths of her money, then spends another $18. She has $12 left. How much did she start with?
Show worked solution
$12 + $18 = $30, which is 3/5 of the start. One fifth is $10, so she started with $50. Check: 2/5 of 50 = 20, 50 − 20 − 18 = 12 ✓.