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Answer Key — Teacher Copy
Mathematics

Fractions: Parts, Equivalence, and Operations Practice

Fractions—parts of a whole, equivalence, comparison, simplification, and operations
Date: July 25, 2026  •  14 questions  •  Total: 92 points
1. Multiple Choice (5 pts)
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?
✓ Answer
A. Add
2. Multiple Choice (5 pts)
Compute: 5/6 − 1/4 = ?
✓ Answer
A. 7/12
3. True / False (2 pts)
The fractions 2/3 and 8/12 are equivalent.
✓ Answer
True
4. Multiple Choice (5 pts)
Which of the following is an improper fraction?
✓ Answer
A. 13/12
5. Fill in the Blank (3 pts)
The fraction with numerator 3 and denominator 10 is _____.
✓ Answer
3/10
6. Word Problem (15 pts)
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.
✎ Worked Solution
Step 1: Total yogurt = servings × yogurt per serving
Step 2: Total yogurt = 7 × 2/5 = 14/5
Step 3: Convert to mixed number: 14/5 = 2 4/5
Answer: 2 4/5 cups
7. Multiple Choice (5 pts)
Which fraction is equivalent to 6/8?
✓ Answer
A. 9/12
8. True / False (2 pts)
A mixed number is always less than 1.
✓ Answer
False
9. Word Problem (15 pts)
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.
✎ Worked Solution
Step 1: Convert to improper fractions: 1 1/4 = 5/4, 2 2/3 = 8/3
Step 2: Find common denominator (12): 5/4 = 15/12, 8/3 = 32/12
Step 3: Add: 15/12 + 32/12 = 47/12
Step 4: Convert to mixed number: 47/12 = 3 11/12
Answer: 3 11/12 miles
10. Fill in the Blank (3 pts)
Reduce 36/48 to lowest terms: _____.
✓ Answer
3/4
11. Multiple Choice (5 pts)
Which fraction is the greatest?
✓ Answer
B. 4/9
12. True / False (2 pts)
On a number line, 5/8 is located to the right of 1/2.
✓ Answer
True
13. Short Answer (10 pts)
In 2–3 sentences, explain the difference between proper fractions, improper fractions, and mixed numbers. Give one example of each.
✓ Answer
Model answer: A proper fraction has a numerator smaller than its denominator (e.g., 3/5), so its value is less than 1. An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4). A mixed number combines a whole number and a proper fraction (e.g., 1 3/4).
14. Word Problem (15 pts)
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.
✎ Worked Solution
Step 1: Number of glasses = total juice ÷ juice per glass
Step 2: Number of glasses = 3 ÷ (3/8)
Step 3: Divide by a fraction: 3 × 8/3 = 8
Answer: 8 full glasses