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Mathematics

Understanding Fractions: Units, Number Lines, and Real-Life Applications

Fractions (unit fractions, numerator/denominator, proper vs. improper, multiplying whole numbers by fractions, measurement and number lines)
Date: September 7, 2026  •  Questions: 40  •  Estimated time: 35 minutes
Score
____ / 100
Student Name
Class / Section
Grade / Year
Teacher
School
Instructions: Read each question carefully and answer to the best of your ability. Show all working for word problems.
1. A fraction represents a part of a whole. (1 pt)
True
False
2. In the fraction 7/10, the number 7 is the denominator. (1 pt)
True
False
3. If a shape is cut into more equal pieces, each piece becomes larger. (1 pt)
True
False
4. Fractions can be shown between whole numbers on a number line. (1 pt)
True
False
5. The fraction 9/9 is an improper fraction. (1 pt)
True
False
6. Folding a strip into four equal sections creates parts of size 1/4 each. (1 pt)
True
False
7. The fraction 3/2 is less than 1. (1 pt)
True
False
8. Fractions were studied in ancient Indian mathematics. (1 pt)
True
False
9. Multiplying 6 by 1/3 results in a number greater than 6. (1 pt)
True
False
10. To plot 2/5 from 0 to 1 on a number line, divide the segment into 5 equal parts and count two parts from 0. (1 pt)
True
False

11. Which of the following is a unit fraction? (2 pts)
A. 2/3
B. 1/6
C. 3/2
D. 5/3
12. Which statement about size is correct? (2 pts)
A. 1/8 is larger than 1/5
B. 1/5 is larger than 1/8
C. 1/8 equals 1/5
D. The two fractions cannot be compared
13. Identify the improper fraction. (2 pts)
A. 4/7
B. 7/4
C. 3/5
D. 5/6
14. The denominator in 11/12 tells you: (2 pts)
A. How many parts are taken
B. The number of equal parts in the whole
C. The whole number part of the quantity
D. Nothing about the size of the parts
15. To locate 5/8 on the interval from 0 to 1, into how many equal parts should the interval be divided? (2 pts)
A. 4
B. 5
C. 8
D. 10
16. Which reading emphasizes the unit fraction idea for 5/6? (2 pts)
A. five groups of one-sixth
B. five and one-sixth
C. five over six times
D. six groups of one-fifth
17. Which fraction is equal to one whole? (2 pts)
A. 7/8
B. 5/5
C. 9/10
D. 4/7
18. A recipe needs 3/4 cup of milk. Which is an equivalent way to measure this using 1/4-cup scoops? (2 pts)
A. one 1/4-cup scoop
B. two 1/4-cup scoops
C. three 1/4-cup scoops
D. four 1/4-cup scoops
19. What is the value of 18 × 1/6? (2 pts)
A. 3
B. 6
C. 12
D. 108
20. Which fraction is closest to 1 but still less than 1? (2 pts)
A. 3/8
B. 5/12
C. 4/7
D. 8/9

21. The top number of a fraction is called the   . (2 pts)
22. The bottom number of a fraction is the   . (2 pts)
23. Each equal piece of a divided whole is a   unit. (2 pts)
24. A fraction with a smaller numerator than its denominator is called   . (2 pts)
25. To multiply a whole number by a fraction, multiply the whole number by the numerator and then   by the denominator. (2 pts)
26. To mark 4/7 between 0 and 1, divide the segment into   equal parts. (2 pts)
27. The fraction 12/12 is equal to   . (2 pts)
28. A builder might measure 1/3 of a board’s length before making a   . (2 pts)
29. Between 1/9 and 1/3, the larger piece is   . (2 pts)
30. Folding a paper into two equal sections makes parts of size   . (2 pts)

31. A roll of ribbon is 5 meters long. If 2/5 of the ribbon is used to wrap a package, how many meters of ribbon are used? Show your working. (5 pts)
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32. A pan of brownies is cut into 12 equal squares. Lina eats 5 squares. What fraction of the pan did she eat? Show your working. (5 pts)
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33. A 2-meter measuring stick is marked in 1/4-meter sections. What is the total length of three consecutive 1/4-meter sections? Show your working. (5 pts)
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Answer:
34. A rope is 12 meters long. A teacher cuts off 1/3 of it for a demonstration. How long is the piece that was cut? Show your working. (5 pts)
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35. A garden row is 9 meters long. If 5/9 of the row is planted with carrots, how many meters are planted with carrots? Show your working. (5 pts)
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36. On a number line from 0 to 1, you want to place the fraction 5/8. Into how many equal parts should you divide the interval, and at which count from 0 will 5/8 be located? Show your working. (5 pts)
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37. You fill a container using a 1/4-cup scoop. After three scoops, what fraction of a cup have you added? Show your working. (5 pts)
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38. A box contains 16 chalk sticks. Each student receives 1/8 of the box. How many chalk sticks does each student get? Show your working. (5 pts)
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39. A paper strip is 6 units long. If 2/3 of the strip is shaded, how many units are shaded? Show your working. (5 pts)
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40. A can of base paint holds 5 liters. To make a tint, you add a color amount equal to 1/10 of the base paint. How many liters of color are added? Show your working. (5 pts)
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Answer: