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Mathematics

Fractions: Concepts and Operations (Grade 6)

Fractions — parts of a whole, equivalence, simplification, comparison, and addition/subtraction
Date: July 25, 2026  •  Questions: 40  •  Estimated time: 60 minutes
Score
____ / 100
Student Name
Class / Section
Grade / Year
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Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1. When a whole is divided into equal parts, each part is a fraction of the whole. (1 pt)
True
False
2. 7/3 is greater than 2. (1 pt)
True
False
3. 0/9 is equal to 0. (1 pt)
True
False
4. Multiplying 2/5 by 2/2 creates an equivalent fraction. (1 pt)
True
False
5. 3/4 and 6/8 represent the same quantity. (1 pt)
True
False
6. To add 1/3 and 1/4, using 7 as a common denominator is correct. (1 pt)
True
False
7. Twenty minutes is one-third of an hour. (1 pt)
True
False
8. A fraction in simplest form has no common factor greater than 1 between its numerator and denominator. (1 pt)
True
False
9. On the number line, 1/4 is to the right of 1/3. (1 pt)
True
False
10. Subtracting 5/6 from 1/2 gives a negative result. (1 pt)
True
False

11. Which fraction is equivalent to 3/5? (2 pts)
A. 9/15
B. 12/25
C. 6/11
D. 15/18
12. 18/24 in lowest terms is: (2 pts)
A. 3/4
B. 2/3
C. 6/8
D. 9/12
13. Which of the following is a mixed number? (2 pts)
A. 11/4
B. 4 2/9
C. 7/7
D. 9/2
14. Which is greater? (2 pts)
A. 5/12
B. 4/9
C. They are equal
D. Cannot be compared
15. 2 3/5 expressed as an improper fraction is: (2 pts)
A. 13/5
B. 12/5
C. 7/5
D. 23/5
16. 3/8 + 1/4 equals: (2 pts)
A. 1/2
B. 5/8
C. 3/12
D. 7/8
17. 9/10 − 7/10 equals: (2 pts)
A. 1/5
B. 2/10
C. 1/10
D. 2/5
18. Arrange in ascending order: 1/2, 3/10, 2/5 (2 pts)
A. 1/2, 2/5, 3/10
B. 3/10, 2/5, 1/2
C. 2/5, 3/10, 1/2
D. 2/5, 1/2, 3/10
19. Find the missing numerator: __/12 = 5/6 (2 pts)
A. 9
B. 10
C. 12
D. 15
20. Which fraction is not in lowest terms? (2 pts)
A. 9/14
B. 4/7
C. 8/12
D. 7/9

21. The fraction "one-half" is written as   . (2 pts)
22. A fraction greater than 1 is called an   fraction. (2 pts)
23. Fifteen minutes is   of an hour. (2 pts)
24. To reduce 21/28 to lowest terms, divide by their   common factor. (2 pts)
25. On a number line, the midpoint between 0 and 1 is   . (2 pts)
26. The least common multiple of 6 and 8 is   . (2 pts)
27. 3 1/4 written as an improper fraction is   . (2 pts)
28. Multiplying the numerator and denominator of 4/9 by   makes a fraction with denominator 27. (2 pts)
29. Between 5/8 and 2/3, the greater fraction is   . (2 pts)
30. A juice mix uses 2/5 L of water and 3/10 L of syrup; the total is   L. (2 pts)

31. A runner jogs 3/5 km in the morning and 1/5 km in the evening. How far does the runner travel in total? Show your working. (5 pts)
Working:
Answer:
32. A pizza is cut into 12 equal slices. Maya eats 5 slices and Omar eats 2 slices. What fraction of the pizza remains? Show your working. (5 pts)
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Answer:
33. What fraction of an hour is 18 minutes? Express your answer in simplest form. Show your working. (5 pts)
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Answer:
34. Ali ran 7/12 km and Bea ran 5/8 km. Who ran farther and by how much (in km)? Show your working. (5 pts)
Working:
Answer:
35. A wooden board is 1 2/3 m long. If 3/4 m is cut off, how much length remains? Show your working. (5 pts)
Working:
Answer:
36. A ribbon 2/3 m long is cut into 3 equal pieces. What is the length of each piece? Show your working. (5 pts)
Working:
Answer:
37. What fraction of a right angle (90°) is 30°? Write your answer in simplest form. Show your working. (5 pts)
Working:
Answer:
38. A 5/6-liter bottle of juice is shared equally among 3 friends. How much juice does each friend get? Show your working. (5 pts)
Working:
Answer:
39. Starting at 0 on a straight path, Riya walks 3/10 km east and then 1/5 km west. Where is she relative to the start? Show your working. (5 pts)
Working:
Answer:
40. A chef wants a total of 5/6 L of marinade. If 2/9 L is lemon juice and the rest is water, how much water must be added? Show your working. (5 pts)
Working:
Answer: