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Mathematics

Fractions Mastery: Parts, Equivalence, and Operations

Fractions—parts of a whole, equivalence, comparison, and basic operations
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False A unit fraction is any fraction with numerator equal to 1.
1 pt
True
False
Answer: True
2.
True / False The fractions 3/5 and 6/10 represent the same value.
1 pt
True
False
Answer: True
3.
True / False A mixed number is always less than 1.
1 pt
True
False
Answer: False
4.
True / False To compare 2/7 and 3/7, you only need to compare the numerators.
1 pt
True
False
Answer: True
5.
True / False Adding 4/9 and 2/9 gives 6/18.
1 pt
True
False
Answer: False
6.
True / False The fraction 5/4 is an improper fraction.
1 pt
True
False
Answer: True
7.
True / False Reducing a fraction to lowest terms changes its value.
1 pt
True
False
Answer: False
8.
True / False Zero can be written as 0/9 for any nonzero denominator.
1 pt
True
False
Answer: True
9.
True / False To add 1/3 and 1/4, you can add the denominators to get 1/7.
1 pt
True
False
Answer: False
10.
True / False On a number line, 5/6 is to the right of 3/4.
1 pt
True
False
Answer: True
11.
Multiple Choice Which of the following is a proper fraction?
2 pts
A. 7/5
B. 9/9
C. 4/7
D. 12/12
Answer: C. 4/7
12.
Multiple Choice Convert 17/5 to a mixed number.
2 pts
A. 3 1/5
B. 3 2/5
C. 2 3/5
D. 4 2/5
Answer: B. 3 2/5
13.
Multiple Choice Which pair are like fractions?
2 pts
A. 3/8 and 5/8
B. 2/7 and 3/9
C. 4/5 and 4/7
D. 1/3 and 2/6
Answer: A. 3/8 and 5/8
14.
Multiple Choice Simplify 18/24 to lowest terms.
2 pts
A. 3/4
B. 2/5
C. 4/9
D. 5/8
Answer: A. 3/4
15.
Multiple Choice What is 2/3 + 1/6?
2 pts
A. 3/9
B. 1/2
C. 5/6
D. 7/6
Answer: C. 5/6
16.
Multiple Choice Which fraction is equal to 0.25?
2 pts
A. 1/3
B. 1/4
C. 2/5
D. 3/8
Answer: B. 1/4
17.
Multiple Choice Which fraction is greatest?
2 pts
A. 3/4
B. 4/5
C. 7/9
D. 5/6
Answer: D. 5/6
18.
Multiple Choice Compute 5/8 − 1/4.
2 pts
A. 1/2
B. 3/8
C. 1/8
D. 5/12
Answer: B. 3/8
19.
Multiple Choice Which is equivalent to 9/12?
2 pts
A. 3/4
B. 2/3
C. 6/10
D. 4/5
Answer: A. 3/4
20.
Multiple Choice The least common denominator of 2/9 and 5/12 is:
2 pts
A. 21
B. 36
C. 108
D. 18
Answer: B. 36
21.
Fill in the Blank The number on the top of a fraction is called the _____.
2 pts
Answer: numerator
22.
Fill in the Blank Fractions with the same denominator are called _____.
2 pts
Answer: like fractions
23.
Fill in the Blank To add 1/5 and 2/3, use a common _____.
2 pts
Answer: denominator
24.
Fill in the Blank The fraction 10/15 in lowest terms is _____.
2 pts
Answer: 2/3
25.
Fill in the Blank One whole written as an improper fraction with denominator 9 is _____.
2 pts
Answer: 9/9
26.
Fill in the Blank The mixed number 4 3/8 written as an improper fraction is _____.
2 pts
Answer: 35/8
27.
Fill in the Blank The fraction halfway between 1/4 and 1/2 is _____.
2 pts
Answer: 3/8
28.
Fill in the Blank The symbol to show 7/11 is greater than 5/11 is _____.
2 pts
Answer: >
29.
Fill in the Blank A fraction with a numerator larger than its denominator is called an _____.
2 pts
Answer: improper fraction
30.
Fill in the Blank The reciprocal of 3/5 is _____.
2 pts
Answer: 5/3
31.
Word Problem A recipe needs 3/4 cup of sugar. You only have 1/2 cup. How much more sugar do you need? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find a common denominator: 1/2 = 2/4
Step 2: Subtract: 3/4 − 2/4 = 1/4
Answer: 1/4 cup more
32.
Word Problem Maya jogs 1 1/4 km in the morning and 3/8 km in the evening. How far does she jog in total each day? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Convert 1 1/4 to an improper fraction: 1 1/4 = 5/4
Step 2: Find common denominator for 5/4 and 3/8: LCD = 8; 5/4 = 10/8
Step 3: Add: 10/8 + 3/8 = 13/8 = 1 5/8
Answer: 1 5/8 km
33.
Word Problem A shelf holds 24 books. If 5/8 of them are fiction, how many fiction books are there? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Multiply total by the fraction: 24 × 5/8
Step 2: Simplify: (24 ÷ 8) × 5 = 3 × 5 = 15
Answer: 15 fiction books
34.
Word Problem How many minutes are in 2/3 of an hour? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: 1 hour = 60 minutes
Step 2: Compute 2/3 of 60: (2/3) × 60 = 40
Answer: 40 minutes
35.
Word Problem What fraction of a full turn (360°) is a right angle (90°)? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Form the fraction: 90/360
Step 2: Simplify by 90: 90/360 = 1/4
Answer: 1/4 of a full turn
36.
Word Problem There are 3 pizzas, each cut into 8 slices. Four friends eat 5 slices each. How many pizzas are left uneaten? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Total slices: 3 × 8 = 24
Step 2: Slices eaten: 4 × 5 = 20
Step 3: Slices remaining: 24 − 20 = 4
Step 4: Convert to pizzas: 4/8 = 1/2 pizza
Answer: 1/2 pizza left
37.
Word Problem Which is greater, 7/12 or 5/8, and by how much? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find a common denominator: LCD of 12 and 8 is 24
Step 2: Convert: 7/12 = 14/24; 5/8 = 15/24
Step 3: Compare and subtract: 15/24 − 14/24 = 1/24
Answer: 5/8 is greater by 1/24
38.
Word Problem A can has 3 1/2 L of paint. You use 1 3/4 L on a wall and 2/5 L for touch-ups. How much paint remains? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Convert to improper fractions: 3 1/2 = 7/2; 1 3/4 = 7/4
Step 2: Express all with LCD 20: 7/2 = 70/20; 7/4 = 35/20; 2/5 = 8/20
Step 3: Subtract: 70/20 − 35/20 − 8/20 = 27/20
Step 4: Convert to mixed number: 27/20 = 1 7/20
Answer: 1 7/20 L remains
39.
Word Problem A class period is 50 minutes. The teacher spends 12 minutes reviewing and 3/10 of the period on group work. How many minutes are left for practice? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Compute group work time: (3/10) × 50 = 15 minutes
Step 2: Total used: 12 + 15 = 27 minutes
Step 3: Remaining: 50 − 27 = 23 minutes
Answer: 23 minutes
40.
Word Problem In a garden, 2/5 is planted with carrots and 1/4 with beans. The rest is for flowers. What fraction is for flowers? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Total fraction planted: 2/5 + 1/4
Step 2: Find LCD 20: 2/5 = 8/20; 1/4 = 5/20
Step 3: Sum planted: 8/20 + 5/20 = 13/20
Step 4: Flowers: 1 − 13/20 = 7/20
Answer: 7/20 of the garden
40
Total Questions
100
Total Points
~35
Minutes