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Mathematics

Fractions: Concepts and Operations (Grade 6)

Fractions — parts of a whole, equivalence, simplification, comparison, and addition/subtraction
100 pts
40 questions • ~60 min
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False When a whole is divided into equal parts, each part is a fraction of the whole.
1 pt
True
False
Answer: True
2.
True / False 7/3 is greater than 2.
1 pt
True
False
Answer: True
3.
True / False 0/9 is equal to 0.
1 pt
True
False
Answer: True
4.
True / False Multiplying 2/5 by 2/2 creates an equivalent fraction.
1 pt
True
False
Answer: True
5.
True / False 3/4 and 6/8 represent the same quantity.
1 pt
True
False
Answer: True
6.
True / False To add 1/3 and 1/4, using 7 as a common denominator is correct.
1 pt
True
False
Answer: False
7.
True / False Twenty minutes is one-third of an hour.
1 pt
True
False
Answer: True
8.
True / False A fraction in simplest form has no common factor greater than 1 between its numerator and denominator.
1 pt
True
False
Answer: True
9.
True / False On the number line, 1/4 is to the right of 1/3.
1 pt
True
False
Answer: False
10.
True / False Subtracting 5/6 from 1/2 gives a negative result.
1 pt
True
False
Answer: True
11.
Multiple Choice Which fraction is equivalent to 3/5?
2 pts
A. 9/15
B. 12/25
C. 6/11
D. 15/18
Answer: A. 9/15
12.
Multiple Choice 18/24 in lowest terms is:
2 pts
A. 3/4
B. 2/3
C. 6/8
D. 9/12
Answer: A. 3/4
13.
Multiple Choice Which of the following is a mixed number?
2 pts
A. 11/4
B. 4 2/9
C. 7/7
D. 9/2
Answer: B. 4 2/9
14.
Multiple Choice Which is greater?
2 pts
A. 5/12
B. 4/9
C. They are equal
D. Cannot be compared
Answer: B. 4/9
15.
Multiple Choice 2 3/5 expressed as an improper fraction is:
2 pts
A. 13/5
B. 12/5
C. 7/5
D. 23/5
Answer: A. 13/5
16.
Multiple Choice 3/8 + 1/4 equals:
2 pts
A. 1/2
B. 5/8
C. 3/12
D. 7/8
Answer: B. 5/8
17.
Multiple Choice 9/10 − 7/10 equals:
2 pts
A. 1/5
B. 2/10
C. 1/10
D. 2/5
Answer: A. 1/5
18.
Multiple Choice Arrange in ascending order: 1/2, 3/10, 2/5
2 pts
A. 1/2, 2/5, 3/10
B. 3/10, 2/5, 1/2
C. 2/5, 3/10, 1/2
D. 2/5, 1/2, 3/10
Answer: B. 3/10, 2/5, 1/2
19.
Multiple Choice Find the missing numerator: __/12 = 5/6
2 pts
A. 9
B. 10
C. 12
D. 15
Answer: B. 10
20.
Multiple Choice Which fraction is not in lowest terms?
2 pts
A. 9/14
B. 4/7
C. 8/12
D. 7/9
Answer: C. 8/12
21.
Fill in the Blank The fraction "one-half" is written as _____.
2 pts
Answer: 1/2
22.
Fill in the Blank A fraction greater than 1 is called an _____ fraction.
2 pts
Answer: improper
23.
Fill in the Blank Fifteen minutes is _____ of an hour.
2 pts
Answer: 1/4
24.
Fill in the Blank To reduce 21/28 to lowest terms, divide by their _____ common factor.
2 pts
Answer: greatest
25.
Fill in the Blank On a number line, the midpoint between 0 and 1 is _____.
2 pts
Answer: 1/2
26.
Fill in the Blank The least common multiple of 6 and 8 is _____.
2 pts
Answer: 24
27.
Fill in the Blank 3 1/4 written as an improper fraction is _____.
2 pts
Answer: 13/4
28.
Fill in the Blank Multiplying the numerator and denominator of 4/9 by _____ makes a fraction with denominator 27.
2 pts
Answer: 3
29.
Fill in the Blank Between 5/8 and 2/3, the greater fraction is _____.
2 pts
Answer: 2/3
30.
Fill in the Blank A juice mix uses 2/5 L of water and 3/10 L of syrup; the total is _____ L.
2 pts
Answer: 7/10
31.
Word Problem 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.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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 What fraction of an hour is 18 minutes? Express your answer in simplest form. Show your working.
5 pts
Working:
Answer:
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 Ali ran 7/12 km and Bea ran 5/8 km. Who ran farther and by how much (in km)? Show your working.
5 pts
Working:
Answer:
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 A wooden board is 1 2/3 m long. If 3/4 m is cut off, how much length remains? Show your working.
5 pts
Working:
Answer:
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 A ribbon 2/3 m long is cut into 3 equal pieces. What is the length of each piece? Show your working.
5 pts
Working:
Answer:
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 What fraction of a right angle (90°) is 30°? Write your answer in simplest form. Show your working.
5 pts
Working:
Answer:
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 A 5/6-liter bottle of juice is shared equally among 3 friends. How much juice does each friend get? Show your working.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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
40
Total Questions
100
Total Points
~60
Minutes