Fractions Quiz: Test Yourself

Try all ten questions before you look at any answers, and write your working down: in fractions, most marks are lost through small slips, not through not knowing the method. Questions 1 to 7 are multiple choice. Questions 8 to 10 need a short written answer. The answers are printed upside down at the foot of the infographic, and the worked answers below explain why each one is right.

Answer: B, how many equal parts the whole is split into. In 5/8 the whole is cut into 8 equal parts; the numerator, 5, counts how many of those parts you have. The denominator names the size of the parts (eighths), which is why it can never be 0.

Answer: C, 9/12. Multiplying the top and bottom of 3/4 by 3 gives 9/12, and multiplying by 3/3 is multiplying by 1, so the value does not change. 4/5 is a trap: it comes from adding 1 to both numbers, which changes the value (0.8 instead of 0.75).

Answer: D, 3/5. The factors of 18 are 1, 2, 3, 6, 9 and 18, and the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. The highest common factor is 6, and 18 ÷ 6 = 3, 30 ÷ 6 = 5. Options A and B, 9/15 and 6/10, are equal to 3/5 but not fully simplified: each can still be divided by 3 or 2.

Answer: B, 11/12. The lowest common multiple of 4 and 3 is 12. 1/4 = 3/12 and 2/3 = 8/12, so the sum is 11/12. Option A, 3/7, is what you get by adding the numerators and the denominators, the most common fraction mistake. A quick check: 2/3 on its own is more than 3/7, so 3/7 cannot be the total.

Answer: A, 13/5. Multiply the whole number by the denominator and add the numerator: 2 × 5 + 3 = 13, over the same denominator, 5. Check by going back: 13 ÷ 5 = 2 remainder 3, which is 2 3/5.

Answer: C, 1/2. Multiply across: 2 × 3 = 6 and 3 × 4 = 12, giving 6/12 = 1/2. Cancelling first is quicker: the 3s cancel, and the 2 and 4 cancel to 1 and 2, leaving 1/2 straight away. Option B, 8/9, is the answer to 2/3 ÷ 3/4, not 2/3 × 3/4.

Answer: D, 6. Keep, change, flip: 3/5 × 10/1 = 30/5 = 6. It makes sense, because the question asks how many tenths fit into 3/5, and 3/5 = 6/10. Option A, 3/50, is what you get by multiplying instead of dividing.

Model answer: 3/8 = 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%. Another route: 1/8 = 0.125, so 3/8 = 3 × 0.125 = 0.375. Both forms are needed for full marks.

Model answer: 300 g. The recipe is for 6 people and you need it for 4, so you need 4/6 = 2/3 of each amount. 2/3 of 450 g is 450 ÷ 3 × 2 = 150 × 2 = 300 g. Check: 450 g for 6 people is 75 g each, and 4 × 75 = 300 g.

Model answer: 5 ÷ 1/2 asks how many halves fit into 5. Each whole contains 2 halves, so 5 wholes contain 10 halves, and 5 ÷ 1/2 = 10. The answer 2 1/2 comes from finding half of 5, which is 5 × 1/2 or 5 ÷ 2, a different question. A good answer explains the 'how many fit' meaning of division.