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Mathematics

Playing with Numbers: Place Value, Divisibility, and Number Sense — Practice Set

Whole numbers, place value, divisibility, factors and multiples (Class 6)
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 Zero is a whole number but not a natural number.
1 pt
True
False
Answer: True
2.
True / False The successor of 9,999 is 10,000.
1 pt
True
False
Answer: True
3.
True / False Whole numbers are closed under subtraction.
1 pt
True
False
Answer: False
4.
True / False In the Indian system, 1,00,000 is called one lakh.
1 pt
True
False
Answer: True
5.
True / False The Roman numeral XL represents 60.
1 pt
True
False
Answer: False
6.
True / False Every prime number greater than 2 is odd.
1 pt
True
False
Answer: True
7.
True / False If a number is divisible by 9, it is always divisible by 3.
1 pt
True
False
Answer: True
8.
True / False The number 1 has exactly two distinct factors.
1 pt
True
False
Answer: False
9.
True / False The additive identity for whole numbers is 1.
1 pt
True
False
Answer: False
10.
True / False Multiplication of whole numbers is commutative.
1 pt
True
False
Answer: True
11.
Multiple Choice Which of the following is the greatest number?
2 pts
A. 705,200
B. 750,020
C. 700,520
D. 705,020
Answer: B. 750,020
12.
Multiple Choice In 403,506, what is the value of the digit 5?
2 pts
A. 5
B. 50
C. 500
D. 5,000
Answer: C. 500
13.
Multiple Choice Which number is divisible by 6?
2 pts
A. 234
B. 245
C. 253
D. 261
Answer: A. 234
14.
Multiple Choice Which Roman numeral equals 94?
2 pts
A. LXLIV
B. XCIV
C. IC
D. XCVIV
Answer: B. XCIV
15.
Multiple Choice The LCM of 12 and 15 is:
2 pts
A. 30
B. 45
C. 60
D. 120
Answer: C. 60
16.
Multiple Choice Which of the following is a composite number?
2 pts
A. 29
B. 31
C. 37
D. 39
Answer: D. 39
17.
Multiple Choice Starting at 0 on a number line, you make 4 jumps of size 7 to the right. Where do you land?
2 pts
A. 21
B. 28
C. 35
D. 42
Answer: B. 28
18.
Multiple Choice Round 8,649 to the nearest thousand.
2 pts
A. 8,000
B. 8,600
C. 8,700
D. 9,000
Answer: D. 9,000
19.
Multiple Choice Evaluate: 5 × (12 − 7) + 3
2 pts
A. 22
B. 28
C. 30
D. 40
Answer: B. 28
20.
Multiple Choice Which is the correct Indian system grouping of 7,200,300?
2 pts
A. 7,20,030
B. 72,00,300
C. 7,200,30
D. 7,20,03,00
Answer: B. 72,00,300
21.
Fill in the Blank The predecessor of 10,000 is _____
2 pts
Answer: 9999
22.
Fill in the Blank The smallest whole number is _____
2 pts
Answer: 0
23.
Fill in the Blank The Roman numeral for 500 is _____
2 pts
Answer: D
24.
Fill in the Blank A number divisible by 10 must end with _____
2 pts
Answer: 0
25.
Fill in the Blank According to the distributive property, a × (b + c) = a×b + a×_____
2 pts
Answer: c
26.
Fill in the Blank The place value of 7 in 7,046 is _____
2 pts
Answer: 7000
27.
Fill in the Blank The sum of the factors of a perfect number equals _____ times the number.
2 pts
Answer: 2
28.
Fill in the Blank Moving left three steps of size 4 on a number line decreases the value by _____
2 pts
Answer: 12
29.
Fill in the Blank A prime number has exactly _____ distinct factors.
2 pts
Answer: 2
30.
Fill in the Blank In the International system, 1,000,000 is read as _____
2 pts
Answer: one million
31.
Word Problem You start at 18 on a number line. Move right 6 steps of 4 units each, then move left 5 steps of 3 units each. Where do you land? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Total right movement = 6 × 4 = 24
Step 2: Total left movement = 5 × 3 = 15
Step 3: Final position = 18 + 24 − 15 = 27
Answer: 27
32.
Word Problem Estimate the sum of 8,649 and 3,378 by rounding each number to the nearest thousand. What is the estimated total? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: 8,649 rounds to 9,000 (nearest thousand)
Step 2: 3,378 rounds to 3,000 (nearest thousand)
Step 3: Estimated sum = 9,000 + 3,000 = 12,000
Answer: 12,000
33.
Word Problem A school has 48 red chairs and 60 blue chairs. They want to arrange each color in rows with the same number of chairs and no chairs left over. What is the greatest number of chairs in each row? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factors: 48 = 2⁴ × 3; 60 = 2² × 3 × 5
Step 2: HCF = 2² × 3 = 12
Step 3: Therefore, maximum chairs per row = 12
Answer: 12
34.
Word Problem Three bells ring every 18, 24, and 30 minutes respectively. If they all ring together at 8:00 a.m., when will they ring together next? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factors: 18 = 2 × 3²; 24 = 2³ × 3; 30 = 2 × 3 × 5
Step 2: LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360 minutes
Step 3: 360 minutes = 6 hours; 8:00 a.m. + 6 hours = 2:00 p.m.
Answer: 2:00 p.m.
35.
Word Problem A factory can pack items in boxes of 45 or in boxes of 60 with no leftovers in either case. What is the smallest number of items the factory can pack to satisfy both conditions? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factors: 45 = 3² × 5; 60 = 2² × 3 × 5
Step 2: LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180
Step 3: The smallest number of items that fits both box sizes exactly is the LCM
Answer: 180
36.
Word Problem Without long division, determine whether 8,415 is divisible by 9 and by 11. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Test for 9: Sum of digits = 8 + 4 + 1 + 5 = 18 (divisible by 9)
Step 2: Test for 11: (8 + 1) − (4 + 5) = 9 − 9 = 0 (multiple of 11)
Step 3: Therefore, 8,415 is divisible by both 9 and 11
Answer: Divisible by 9: Yes; Divisible by 11: Yes
37.
Word Problem Convert 3,06,50,090 (Indian system) to the International system and write it in words (International system). Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: 3,06,50,090 = 3 crore + 6 lakh + 50 thousand + 90
Step 2: 3 crore = 30,000,000; 6 lakh = 600,000; total = 30,600,000 + 50,000 + 90 = 30,650,090
Step 3: In International format: 30,650,090 = thirty million six hundred fifty thousand ninety
Answer: 30,650,090; Thirty million six hundred fifty thousand ninety
38.
Word Problem Evaluate the expression using brackets: 7 × (18 − 5) − 4 × (6 + 1). Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Compute inside brackets: (18 − 5) = 13 and (6 + 1) = 7
Step 2: Multiply: 7 × 13 = 91 and 4 × 7 = 28
Step 3: Subtract: 91 − 28 = 63
Answer: 63
39.
Word Problem In a 3×3 grid, the numbers are: Row 1: 11, 14, 9 Row 2: 8, 20, 13 Row 3: 7, 16, 10 A supercell is larger than its neighbors directly above, below, left, and right. Is 20 a supercell? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Identify neighbors of 20: up = 14, down = 16, left = 8, right = 13
Step 2: Compare: 20 > 14, 20 > 16, 20 > 8, 20 > 13
Step 3: Since 20 is greater than all four neighbors, it is a supercell
Answer: Yes, 20 is a supercell
40.
Word Problem Find the smallest 5-digit number that is divisible by both 12 and 15. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: LCM(12, 15) = 60 (since 12 = 2² × 3 and 15 = 3 × 5, LCM = 2² × 3 × 5 = 60)
Step 2: Smallest 5-digit number is 10,000; compute 10,000 ÷ 60 ≈ 166.66, so take next whole number 167
Step 3: 167 × 60 = 10,020
Answer: 10,020
40
Total Questions
100
Total Points
~35
Minutes