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Answer Key — Teacher Copy
Mathematics

Fractions: Concepts and Operations (Grade 6)

Fractions — parts of a whole, equivalence, simplification, comparison, and addition/subtraction
Date: July 25, 2026  •  40 questions  •  Total: 100 points
1. True / False (1 pts)
When a whole is divided into equal parts, each part is a fraction of the whole.
✓ Answer
True
2. True / False (1 pts)
7/3 is greater than 2.
✓ Answer
True
3. True / False (1 pts)
0/9 is equal to 0.
✓ Answer
True
4. True / False (1 pts)
Multiplying 2/5 by 2/2 creates an equivalent fraction.
✓ Answer
True
5. True / False (1 pts)
3/4 and 6/8 represent the same quantity.
✓ Answer
True
6. True / False (1 pts)
To add 1/3 and 1/4, using 7 as a common denominator is correct.
✓ Answer
False
7. True / False (1 pts)
Twenty minutes is one-third of an hour.
✓ Answer
True
8. True / False (1 pts)
A fraction in simplest form has no common factor greater than 1 between its numerator and denominator.
✓ Answer
True
9. True / False (1 pts)
On the number line, 1/4 is to the right of 1/3.
✓ Answer
False
10. True / False (1 pts)
Subtracting 5/6 from 1/2 gives a negative result.
✓ Answer
True
11. Multiple Choice (2 pts)
Which fraction is equivalent to 3/5?
✓ Answer
A. 9/15
12. Multiple Choice (2 pts)
18/24 in lowest terms is:
✓ Answer
A. 3/4
13. Multiple Choice (2 pts)
Which of the following is a mixed number?
✓ Answer
B. 4 2/9
14. Multiple Choice (2 pts)
Which is greater?
✓ Answer
B. 4/9
15. Multiple Choice (2 pts)
2 3/5 expressed as an improper fraction is:
✓ Answer
A. 13/5
16. Multiple Choice (2 pts)
3/8 + 1/4 equals:
✓ Answer
B. 5/8
17. Multiple Choice (2 pts)
9/10 − 7/10 equals:
✓ Answer
A. 1/5
18. Multiple Choice (2 pts)
Arrange in ascending order: 1/2, 3/10, 2/5
✓ Answer
B. 3/10, 2/5, 1/2
19. Multiple Choice (2 pts)
Find the missing numerator: __/12 = 5/6
✓ Answer
B. 10
20. Multiple Choice (2 pts)
Which fraction is not in lowest terms?
✓ Answer
C. 8/12
21. Fill in the Blank (2 pts)
The fraction "one-half" is written as _____.
✓ Answer
1/2
22. Fill in the Blank (2 pts)
A fraction greater than 1 is called an _____ fraction.
✓ Answer
improper
23. Fill in the Blank (2 pts)
Fifteen minutes is _____ of an hour.
✓ Answer
1/4
24. Fill in the Blank (2 pts)
To reduce 21/28 to lowest terms, divide by their _____ common factor.
✓ Answer
greatest
25. Fill in the Blank (2 pts)
On a number line, the midpoint between 0 and 1 is _____.
✓ Answer
1/2
26. Fill in the Blank (2 pts)
The least common multiple of 6 and 8 is _____.
✓ Answer
24
27. Fill in the Blank (2 pts)
3 1/4 written as an improper fraction is _____.
✓ Answer
13/4
28. Fill in the Blank (2 pts)
Multiplying the numerator and denominator of 4/9 by _____ makes a fraction with denominator 27.
✓ Answer
3
29. Fill in the Blank (2 pts)
Between 5/8 and 2/3, the greater fraction is _____.
✓ Answer
2/3
30. Fill in the Blank (2 pts)
A juice mix uses 2/5 L of water and 3/10 L of syrup; the total is _____ L.
✓ Answer
7/10
31. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Add like denominators: 3/5 + 1/5 = (3 + 1)/5
Step 2: Simplify the sum: 4/5
Answer: 4/5 km
32. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Total eaten = (5 + 2)/12 = 7/12
Step 2: Remaining fraction = 1 − 7/12 = 5/12
Answer: 5/12 of the pizza remains
33. Word Problem (5 pts)
What fraction of an hour is 18 minutes? Express your answer in simplest form. Show your working.
✎ Worked Solution
Step 1: Write the fraction of the hour: 18/60
Step 2: Simplify by dividing by 6: 18/60 = 3/10
Answer: 3/10 of an hour
34. Word Problem (5 pts)
Ali ran 7/12 km and Bea ran 5/8 km. Who ran farther and by how much (in km)? Show your working.
✎ Worked Solution
Step 1: Find a common denominator (24): 7/12 = 14/24, 5/8 = 15/24
Step 2: Compare and find difference: 15/24 − 14/24 = 1/24
Answer: Bea ran farther by 1/24 km
35. Word Problem (5 pts)
A wooden board is 1 2/3 m long. If 3/4 m is cut off, how much length remains? Show your working.
✎ Worked Solution
Step 1: Convert 1 2/3 to improper: 1 2/3 = 5/3
Step 2: Subtract with common denominator 12: 5/3 = 20/12, 3/4 = 9/12, so 20/12 − 9/12 = 11/12
Answer: 11/12 m remains
36. Word Problem (5 pts)
A ribbon 2/3 m long is cut into 3 equal pieces. What is the length of each piece? Show your working.
✎ Worked Solution
Step 1: Divide 2/3 by 3: 2/3 ÷ 3 = 2/3 × 1/3
Step 2: Multiply numerators and denominators: 2/9
Answer: Each piece is 2/9 m
37. Word Problem (5 pts)
What fraction of a right angle (90°) is 30°? Write your answer in simplest form. Show your working.
✎ Worked Solution
Step 1: Form the fraction: 30/90
Step 2: Simplify by dividing by 30: 1/3
Answer: 1/3 of a right angle
38. Word Problem (5 pts)
A 5/6-liter bottle of juice is shared equally among 3 friends. How much juice does each friend get? Show your working.
✎ Worked Solution
Step 1: Divide 5/6 by 3: 5/6 ÷ 3 = 5/6 × 1/3
Step 2: Compute: 5/18
Answer: Each friend gets 5/18 L
39. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Convert 1/5 to tenths: 1/5 = 2/10
Step 2: Net displacement: 3/10 − 2/10 = 1/10
Answer: 1/10 km east of the start
40. Word Problem (5 pts)
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.
✎ Worked Solution
Step 1: Rewrite 5/6 with denominator 18: 5/6 = 15/18; 2/9 = 4/18
Step 2: Find missing part: 15/18 − 4/18 = 11/18
Answer: 11/18 L of water