Generated Jul 25, 2026 at 12:07 PM from fractions.pdf
Mathematics
Fractions: Parts, Equivalence, and Operations Practice
Fractions—parts of a whole, equivalence, comparison, simplification, and operations
92 pts
14 questions • ~35 min
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
5 pts
Multiple Choice
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?
A. Add
B. Subtract
C. Multiply
D. Divide
Answer:
A. Add
2.
5 pts
Multiple Choice
Compute: 5/6 − 1/4 = ?
A. 7/12
B. 3/10
C. 2/3
D. 9/10
Answer:
A. 7/12
3.
2 pts
True / False
The fractions 2/3 and 8/12 are equivalent.
True
False
Answer:
True
4.
5 pts
Multiple Choice
Which of the following is an improper fraction?
A. 13/12
B. 4/5
C. 2/3
D. 5/6
Answer:
A. 13/12
5.
3 pts
Fill in the Blank
The fraction with numerator 3 and denominator 10 is _____.
Answer:
3/10
6.
15 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Multiple Choice
Which fraction is equivalent to 6/8?
A. 9/12
B. 12/18
C. 8/14
D. 5/6
Answer:
A. 9/12
8.
2 pts
True / False
A mixed number is always less than 1.
True
False
Answer:
False
9.
15 pts
Word Problem
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.
Working:
Answer:
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.
3 pts
Fill in the Blank
Reduce 36/48 to lowest terms: _____.
Answer:
3/4
11.
5 pts
Multiple Choice
Which fraction is the greatest?
A. 3/7
B. 4/9
C. 5/12
D. 2/5
Answer:
B. 4/9
12.
2 pts
True / False
On a number line, 5/8 is located to the right of 1/2.
True
False
Answer:
True
13.
10 pts
Short Answer
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.
15 pts
Word Problem
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.
Working:
Answer:
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
14
Total Questions
92
Total Points
~35
Minutes