Fractions & Decimals
71 Class 6 IMO Mathematics Olympiad practice questions on fractions & decimals, part of the Arithmetic topic area. Every question below includes the correct answer and a full explanation.
Practice this topic interactively →1. What is 1/2 + 1/4?
- A.1/6
- B.2/6
- C.3/4
- D.1
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Answer: C. 3/4
1/2 = 2/4, so 2/4 + 1/4 = 3/4.
2. Convert 3/5 to a decimal.
- A.0.35
- B.0.5
- C.0.6
- D.0.65
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Answer: C. 0.6
3 ÷ 5 = 0.6.
3. Which fraction is equivalent to 0.25?
- A.1/2
- B.1/4
- C.1/5
- D.1/8
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Answer: B. 1/4
1 ÷ 4 = 0.25.
4. Which is smaller: 0.6 or 0.55?
- A.0.6
- B.0.55
- C.They are equal
- D.Cannot tell
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Answer: B. 0.55
0.55 has a smaller tenths digit (5) than 0.6 (6).
5. 0.75 + 1.6 =
- A.2.25
- B.2.35
- C.2.45
- D.2.55
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Answer: B. 2.35
0.75 + 1.60 = 2.35.
6. Which fraction is equal to 0.6?
- A.2/5
- B.3/5
- C.4/5
- D.5/6
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Answer: B. 3/5
3 ÷ 5 = 0.6.
7. What is 4/10 − 3/10?
- A.0.2
- B.0.1
- C.0
- D.0.3
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Answer: B. 0.1
4/10 − 3/10 = 1/10 = 0.1.
8. What is 6/10 + 4/10?
- A.1.2
- B.1.0
- C.1.1
- D.0.9
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Answer: B. 1.0
6/10 + 4/10 = 10/10 = 1.0.
9. What is 5/10 + 1/10?
- A.0.7
- B.0.6
- C.0.8
- D.0.5
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Answer: B. 0.6
5/10 + 1/10 = 6/10 = 0.6.
10. What is 9/10 − 2/10?
- A.0.7
- B.0.6
- C.0.8
- D.0.9
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Answer: A. 0.7
9/10 − 2/10 = 7/10 = 0.7.
11. What is 1.25 × 2?
- A.2.75
- B.2.25
- C.3.5
- D.2.5
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Answer: D. 2.5
1.25 × 2 = 2.5.
12. Which fraction represents 6/10?
- A.6/100
- B.4/10
- C.6/10
- D.7/10
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Answer: C. 6/10
The fraction 6/10 represents itself directly.
13. What is 7/10 + 5/10?
- A.1.3
- B.1.1
- C.1.4
- D.1.2
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Answer: D. 1.2
7/10 + 5/10 = 12/10 = 1.2.
14. What is 6/10 + 6/10?
- A.1.2
- B.1.1
- C.1.4
- D.1.3
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Answer: A. 1.2
6/10 + 6/10 = 12/10 = 1.2.
15. What decimal represents 375/1000?
- A.0.35
- B.0.425
- C.0.4
- D.0.375
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Answer: D. 0.375
375 ÷ 1000 = 0.375.
16. A school has 480 students. If 6/12 are in a club, how many students are in the club?
- A.280
- B.220
- C.240
- D.260
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Answer: C. 240
480 × 6/12 = 240 students.
17. What fraction of the grid shown is shaded?
- A.1/5
- B.2/5
- C.3/5
- D.4/5
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Answer: B. 2/5
4 out of 10 squares are shaded: 4/10 = 2/5.
18. What fraction of the grid shown is shaded?
- A.1/3
- B.1/2
- C.2/3
- D.3/4
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Answer: B. 1/2
6 out of 12 squares are shaded: 6/12 = 1/2.
19. What fraction of the grid shown is shaded?
- A.3/5
- B.4/5
- C.2/3
- D.5/6
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Answer: B. 4/5
12 out of 15 squares are shaded: 12/15 = 4/5.
20. What is 2/3 − 1/6?
- A.1/3
- B.1/2
- C.2/3
- D.5/6
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Answer: B. 1/2
2/3 = 4/6, so 4/6 − 1/6 = 3/6 = 1/2.
21. What is 1/3 + 1/6?
- A.1/9
- B.1/2
- C.2/9
- D.1/3
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Answer: B. 1/2
1/3 = 2/6, so 2/6 + 1/6 = 3/6 = 1/2.
22. Convert 7/20 to a decimal.
- A.0.35
- B.0.7
- C.0.14
- D.3.5
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Answer: A. 0.35
7 ÷ 20 = 0.35.
23. What is 1.25 − 0.6?
- A.0.55
- B.0.65
- C.0.75
- D.1.85
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Answer: B. 0.65
1.25 − 0.60 = 0.65.
24. Which fraction is greatest?
- A.7/12
- B.5/8
- C.9/16
- D.2/3
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Answer: D. 2/3
Using 48ths: 7/12=28/48, 5/8=30/48, 9/16=27/48, 2/3=32/48 — 2/3 is greatest.
25. If 3/5 of a number is 27, what is the number?
- A.36
- B.40
- C.45
- D.50
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Answer: C. 45
27 ÷ 3 × 5 = 45.
26. Which decimal is equal to 3/8?
- A.0.325
- B.0.35
- C.0.375
- D.0.385
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Answer: C. 0.375
3 ÷ 8 = 0.375.
27. A recipe needs 3/4 kg flour. How much flour is needed for 4 identical batches?
- A.2 kg
- B.2.5 kg
- C.3 kg
- D.3.5 kg
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Answer: C. 3 kg
3/4 × 4 = 3 kg.
28. Which fraction is equivalent to 0.6?
- A.6/100
- B.7/10
- C.4/10
- D.6/10
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Answer: D. 6/10
0.6 means 6 tenths, so it equals 6/10.
29. What is 1.5 × 2?
- A.2.75
- B.3.25
- C.4.0
- D.3.0
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Answer: D. 3.0
1.5 × 2 = 3.0.
30. Which fraction equals 9/10 in simplest form?
- A.9/10
- B.10/10
- C.9/100
- D.1/10
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Answer: A. 9/10
9 and 10 share no common factor here, so 9/10 is already in simplest form.
31. What decimal represents 150/1000?
- A.0.175
- B.0.2
- C.0.125
- D.0.15
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Answer: D. 0.15
150 ÷ 1000 = 0.15.
32. Which fraction equals 3/10 in simplest form?
- A.7/10
- B.4/10
- C.3/10
- D.3/100
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Answer: C. 3/10
3 and 10 share no common factor here, so 3/10 is already in simplest form.
33. What is 6/10 − 2/10?
- A.0.3
- B.0.6
- C.0.4
- D.0.5
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Answer: C. 0.4
6/10 − 2/10 = 4/10 = 0.4.
34. Which fraction represents 2/10?
- A.3/10
- B.2/10
- C.8/10
- D.2/100
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Answer: B. 2/10
The fraction 2/10 represents itself directly.
35. What is 7/10 − 5/10?
- A.0.4
- B.0.3
- C.0.2
- D.0.1
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Answer: C. 0.2
7/10 − 5/10 = 2/10 = 0.2.
36. A school has 480 students. If 4/12 are in a club, how many students are in the club?
- A.140
- B.200
- C.160
- D.180
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Answer: C. 160
480 × 4/12 = 160 students.
37. What fraction of the grid shown is shaded?
- A.1/2
- B.5/8
- C.3/4
- D.5/16
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Answer: B. 5/8
10 out of 16 squares are shaded: 10/16 = 5/8.
38. In the grid shown, what fraction is NOT shaded?
- A.1/4
- B.1/3
- C.3/4
- D.2/3
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Answer: A. 1/4
9 of 12 squares are shaded, so 3 are unshaded: 3/12 = 1/4.
39. Arrange in increasing order: 3/4, 0.6, 7/10
- A.0.6, 7/10, 3/4
- B.3/4, 7/10, 0.6
- C.7/10, 0.6, 3/4
- D.0.6, 3/4, 7/10
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Answer: A. 0.6, 7/10, 3/4
As decimals: 3/4=0.75, 0.6=0.6, 7/10=0.7. In increasing order: 0.6, 0.7, 0.75.
40. A recipe needs 2/3 cup of sugar. How much sugar is needed to make half the recipe?
- A.1/6
- B.1/3
- C.1/2
- D.2/3
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Answer: B. 1/3
2/3 × 1/2 = 2/6 = 1/3.
41. What is 0.4 + 3/10, expressed as a decimal?
- A.0.34
- B.0.43
- C.0.7
- D.4.3
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Answer: C. 0.7
3/10 = 0.3, and 0.4 + 0.3 = 0.7.
42. Which of these is greatest: 5/6, 7/8, 3/4?
- A.5/6
- B.7/8
- C.3/4
- D.They are equal
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Answer: B. 7/8
Using 24ths: 5/6=20/24, 7/8=21/24, 3/4=18/24 — 7/8 is greatest.
43. A ribbon is 3/4 m long. It is cut into 3 equal pieces. How long is each piece?
- A.1/12 m
- B.1/4 m
- C.1/3 m
- D.1/2 m
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Answer: B. 1/4 m
3/4 ÷ 3 = 3/12 = 1/4 m.
44. Which decimal is equal to 9/4?
- A.0.225
- B.2.25
- C.2.4
- D.4.9
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Answer: B. 2.25
9 ÷ 4 = 2.25.
45. What is 2/5 of 45?
- A.9
- B.15
- C.18
- D.20
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Answer: C. 18
45 ÷ 5 = 9, and 9 × 2 = 18.
46. What is 2/10 + 1/10?
- A.0.2
- B.0.3
- C.0.4
- D.0.5
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Answer: B. 0.3
2/10 + 1/10 = 3/10 = 0.3.
47. What decimal represents 25/1000?
- A.0.025
- B.0.05
- C.0
- D.0.075
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Answer: A. 0.025
25 ÷ 1000 = 0.025.
48. What is 9/10 − 7/10?
- A.0.1
- B.0.4
- C.0.3
- D.0.2
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Answer: D. 0.2
9/10 − 7/10 = 2/10 = 0.2.
49. What is 7/10 + 4/10?
- A.1.1
- B.1.3
- C.1.2
- D.1.0
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Answer: A. 1.1
7/10 + 4/10 = 11/10 = 1.1.
50. What is 8/10 − 6/10?
- A.0.2
- B.0.4
- C.0.3
- D.0.1
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Answer: A. 0.2
8/10 − 6/10 = 2/10 = 0.2.
51. Which fraction is equivalent to 0.3?
- A.4/10
- B.7/10
- C.3/100
- D.3/10
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Answer: D. 3/10
0.3 means 3 tenths, so it equals 3/10.
52. What decimal represents 500/1000?
- A.0.475
- B.0.55
- C.0.5
- D.0.525
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Answer: C. 0.5
500 ÷ 1000 = 0.5.
53. What is 3/10 + 5/10?
- A.0.7
- B.0.9
- C.0.8
- D.1.0
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Answer: C. 0.8
3/10 + 5/10 = 8/10 = 0.8.
54. What is 7/10 − 6/10?
- A.0.3
- B.0.1
- C.0.2
- D.0
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Answer: B. 0.1
7/10 − 6/10 = 1/10 = 0.1.
55. What decimal represents 250/1000?
- A.0.3
- B.0.275
- C.0.25
- D.0.225
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Answer: C. 0.25
250 ÷ 1000 = 0.25.
56. What is 0.5 × 2?
- A.1.0
- B.1.25
- C.0.75
- D.2.0
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Answer: A. 1.0
0.5 × 2 = 1.0.
57. What is 4/10 + 3/10?
- A.0.9
- B.0.8
- C.0.6
- D.0.7
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Answer: D. 0.7
4/10 + 3/10 = 7/10 = 0.7.
58. Which fraction represents 8/10?
- A.2/10
- B.9/10
- C.8/10
- D.8/100
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Answer: C. 8/10
The fraction 8/10 represents itself directly.
59. A school has 480 students. If 3/12 are in a club, how many students are in the club?
- A.160
- B.100
- C.140
- D.120
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Answer: D. 120
480 × 3/12 = 120 students.
60. A tank is 3/8 full. After adding 15 more litres, it becomes 5/8 full. What is the total capacity of the tank?
- A.45
- B.60
- C.75
- D.90
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Answer: B. 60
The difference, 5/8 − 3/8 = 1/4 of the tank, equals 15 litres. So the full tank is 15 × 4 = 60 litres.
61. What is 0.25 × 2?
- A.0.5
- B.0.75
- C.1.5
- D.0.25
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Answer: A. 0.5
0.25 × 2 = 0.5.
62. Which fraction represents 4/10?
- A.4/10
- B.6/10
- C.4/100
- D.5/10
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Answer: A. 4/10
The fraction 4/10 represents itself directly.
63. Which fraction is equivalent to 0.8?
- A.8/10
- B.9/10
- C.8/100
- D.2/10
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Answer: A. 8/10
0.8 means 8 tenths, so it equals 8/10.
64. What decimal represents 75/1000?
- A.0.075
- B.0.05
- C.0.125
- D.0.1
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Answer: A. 0.075
75 ÷ 1000 = 0.075.
65. What is 2.5 × 2?
- A.5.0
- B.5.25
- C.6.0
- D.4.75
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Answer: A. 5.0
2.5 × 2 = 5.0.
66. Which fraction is equivalent to 0.4?
- A.4/10
- B.4/100
- C.5/10
- D.6/10
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Answer: A. 4/10
0.4 means 4 tenths, so it equals 4/10.
67. What is 9/10 − 5/10?
- A.0.6
- B.0.3
- C.0.5
- D.0.4
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Answer: D. 0.4
9/10 − 5/10 = 4/10 = 0.4.
68. Which fraction is equivalent to 0.2?
- A.2/10
- B.8/10
- C.3/10
- D.2/100
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Answer: A. 2/10
0.2 means 2 tenths, so it equals 2/10.
69. What is 2/10 + 6/10?
- A.0.8
- B.0.9
- C.1.0
- D.0.7
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Answer: A. 0.8
2/10 + 6/10 = 8/10 = 0.8.
70. A school has 480 students. If 2/12 are in a club, how many students are in the club?
- A.60
- B.120
- C.100
- D.80
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Answer: D. 80
480 × 2/12 = 80 students.
71. A school has 480 students. If 5/12 are in a club, how many students are in the club?
- A.220
- B.180
- C.200
- D.240
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Answer: C. 200
480 × 5/12 = 200 students.