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Mathematics

Fractions: Parts, Equivalence, and Operations Practice

Fractions—parts of a whole, equivalence, comparison, simplification, and operations
Date: July 25, 2026  •  Questions: 14  •  Estimated time: 35 minutes
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Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1. Lena sipped 2/3 of her smoothie in the morning and another 1/6 in the afternoon. To find the total fraction she drank, which operation should you use? (5 pts)
A. Add
B. Subtract
C. Multiply
D. Divide
2. Compute: 5/6 − 1/4 = ? (5 pts)
A. 7/12
B. 3/10
C. 2/3
D. 9/10

3. The fractions 2/3 and 8/12 are equivalent. (2 pts)
True
False

4. Which of the following is an improper fraction? (5 pts)
A. 13/12
B. 4/5
C. 2/3
D. 5/6

5. The fraction with numerator 3 and denominator 10 is   . (3 pts)

6. A smoothie recipe requires 2/5 cup of yogurt per serving. If Omar makes 7 servings, how much yogurt will he use in total? Show your working. (15 pts)
Working:
Answer:

7. Which fraction is equivalent to 6/8? (5 pts)
A. 9/12
B. 12/18
C. 8/14
D. 5/6

8. A mixed number is always less than 1. (2 pts)
True
False

9. A hiker travels 1 1/4 miles before lunch and 2 2/3 miles after lunch. How far does the hiker travel in total? Show your working. (15 pts)
Working:
Answer:

10. Reduce 36/48 to lowest terms:   . (3 pts)

11. Which fraction is the greatest? (5 pts)
A. 3/7
B. 4/9
C. 5/12
D. 2/5

12. On a number line, 5/8 is located to the right of 1/2. (2 pts)
True
False

13. In 2–3 sentences, explain the difference between proper fractions, improper fractions, and mixed numbers. Give one example of each. (10 pts)

14. A pitcher holds 3 liters of juice. Each glass holds 3/8 liter. How many full glasses can be poured from the pitcher? Show your working. (15 pts)
Working:
Answer: