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Mathematics

Playing With Numbers: Class 6 Mixed Practice

Number systems, numeration, factors and multiples, properties, and Roman numerals
100 pts
40 questions • ~45 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.
1 pt
True
False
Answer: True
2.
True / False In the set of whole numbers, 0 has a predecessor.
1 pt
True
False
Answer: False
3.
True / False Addition of whole numbers is commutative.
1 pt
True
False
Answer: True
4.
True / False Subtraction of whole numbers is associative.
1 pt
True
False
Answer: False
5.
True / False Whole numbers are closed under multiplication.
1 pt
True
False
Answer: True
6.
True / False In the Indian system, the number 12,34,567 is correctly grouped with commas.
1 pt
True
False
Answer: True
7.
True / False The number 1 is a prime number.
1 pt
True
False
Answer: False
8.
True / False Every even number is divisible by 4.
1 pt
True
False
Answer: False
9.
True / False 999 rounded to the nearest thousand is 1000.
1 pt
True
False
Answer: True
10.
True / False A number is divisible by 3 if the sum of its digits is a multiple of 3.
1 pt
True
False
Answer: True
11.
Multiple Choice Which number is the greatest?
2 pts
A. 607
B. 670
C. 706
D. 760
Answer: D. 760
12.
Multiple Choice In 3,58,241 (Indian system), the place value of the digit 5 is:
2 pts
A. 5,000
B. 50,000
C. 500
D. 5,00,000
Answer: B. 50,000
13.
Multiple Choice Write 27,05,300 (Indian system) in the International system.
2 pts
A. 270,530
B. 2,705,300
C. 27,053,00
D. 27,530,0
Answer: B. 2,705,300
14.
Multiple Choice Round 46,372 to the nearest 1,000.
2 pts
A. 46,300
B. 46,000
C. 47,000
D. 46,500
Answer: B. 46,000
15.
Multiple Choice Evaluate: 18 − [6 + 2 × (7 − 4)]
2 pts
A. 0
B. 3
C. 6
D. 12
Answer: C. 6
16.
Multiple Choice Which is the correct Roman numeral for 90?
2 pts
A. IC
B. LXXXX
C. XC
D. VC
Answer: C. XC
17.
Multiple Choice Which of the following is a prime number?
2 pts
A. 77
B. 97
C. 91
D. 121
Answer: B. 97
18.
Multiple Choice Which number is divisible by 9?
2 pts
A. 7,245
B. 8,137
C. 9,114
D. 7,001
Answer: A. 7,245
19.
Multiple Choice The HCF of 36 and 60 is:
2 pts
A. 6
B. 12
C. 18
D. 24
Answer: B. 12
20.
Multiple Choice How many 4-digit numbers exist?
2 pts
A. 900
B. 999
C. 9,000
D. 10,000
Answer: C. 9,000
21.
Fill in the Blank Zero is the smallest _____ number.
2 pts
Answer: whole
22.
Fill in the Blank The successor of 4,999 is _____.
2 pts
Answer: 5000
23.
Fill in the Blank In the Indian system, 1,00,000 is called one _____.
2 pts
Answer: lakh
24.
Fill in the Blank The additive identity for whole numbers is _____.
2 pts
Answer: 0
25.
Fill in the Blank 300 + 20 + 5 in standard form is _____.
2 pts
Answer: 325
26.
Fill in the Blank A number divisible by 2 and 5 is always divisible by _____.
2 pts
Answer: 10
27.
Fill in the Blank The prime factorization of 84 is 2 × 2 × 3 × _____.
2 pts
Answer: 7
28.
Fill in the Blank In Roman numerals, 40 is written as _____.
2 pts
Answer: XL
29.
Fill in the Blank The place value of 9 in 5,19,804 (Indian system) is _____.
2 pts
Answer: 9000
30.
Fill in the Blank On a number line, moving 7 units left from 15 lands on _____.
2 pts
Answer: 8
31.
Word Problem On Saturday, 48,376 people visited a fair, and on Sunday, 51,942 people visited. Estimate the total number of visitors to the nearest thousand. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Round each to the nearest 1,000: 48,376 → 48,000 and 51,942 → 52,000
Step 2: Add the rounded numbers: 48,000 + 52,000 = 100,000
Answer: Approximately 100,000 visitors
32.
Word Problem A teacher has 84 pencils and 126 erasers. She wants to make identical sets with no items left over. What is the maximum number of sets she can make, and how many pencils and erasers will each set contain? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factorize: 84 = 2 × 2 × 3 × 7; 126 = 2 × 3 × 3 × 7
Step 2: HCF = 2 × 3 × 7 = 42
Step 3: Number of sets = 42; Pencils per set = 84 ÷ 42 = 2; Erasers per set = 126 ÷ 42 = 3
Answer: 42 sets; each set has 2 pencils and 3 erasers
33.
Word Problem Two shuttle buses leave a station at 8:00 AM. One returns every 12 minutes and the other every 15 minutes. At what time will they next arrive together? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 12 and 15: 12 = 2^2 × 3; 15 = 3 × 5 → LCM = 2^2 × 3 × 5 = 60
Step 2: Add 60 minutes to 8:00 AM → 9:00 AM
Answer: 9:00 AM
34.
Word Problem What is the least number that must be subtracted from 5,237 to make it divisible by 6? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: For divisibility by 6, the number must be even and the sum of digits must be a multiple of 3
Step 2: Try subtracting the smallest numbers:
- 5,237 − 1 = 5,236 (even), sum = 5+2+3+6 = 16 (not multiple of 3)
- 5,237 − 2 = 5,235 (odd)
- 5,237 − 3 = 5,234 (even), sum = 14 (not multiple of 3)
- 5,237 − 4 = 5,233 (odd)
- 5,237 − 5 = 5,232 (even), sum = 5+2+3+2 = 12 (multiple of 3)
Answer: 5
35.
Word Problem Find the LCM of 48 and 180 using prime factorization. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factorize: 48 = 2^4 × 3; 180 = 2^2 × 3^2 × 5
Step 2: Take highest powers: LCM = 2^4 × 3^2 × 5 = 16 × 9 × 5
Step 3: Compute: 16 × 9 = 144; 144 × 5 = 720
Answer: 720
36.
Word Problem A shop calculates a bill as (250 + 75) × 4 − 180. Find the final amount. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Evaluate inside brackets: 250 + 75 = 325
Step 2: Multiply: 325 × 4 = 1,300
Step 3: Subtract: 1,300 − 180 = 1,120
Answer: 1,120
37.
Word Problem Convert the number 2,019 to Roman numerals. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Decompose 2,019 = 2,000 + 10 + 9
Step 2: Convert each part: 2,000 = MM; 10 = X; 9 = IX
Step 3: Combine: MM + X + IX = MMXIX
Answer: MMXIX
38.
Word Problem Write 4,57,20,608 (Indian system) in the International system with commas. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Interpret Indian groups: 4 crore = 40,000,000; 57 lakh = 5,700,000; 20 thousand = 20,000; plus 608
Step 2: Add: 40,000,000 + 5,700,000 = 45,700,000; +20,000 = 45,720,000; +608 = 45,720,608
Answer: 45,720,608
39.
Word Problem On a number line, starting at 0, make 5 jumps of 7 units to the right, then 3 jumps of 4 units to the left. Where do you land? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Rightward movement: 5 × 7 = 35 → position 35
Step 2: Leftward movement: 3 × 4 = 12 → move to 35 − 12
Step 3: Compute: 35 − 12 = 23
Answer: 23
40.
Word Problem In the 3×3 grid below, a supercell is a number larger than all of its existing neighbors directly above, below, left, and right. Grid: 12 35 18 44 29 31 27 33 20 Identify all supercells. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Check 35 (top middle): neighbors 12 (left), 18 (right), 29 (down) → 35 > 12, 18, 29 → supercell
Step 2: Check 44 (middle left): neighbors 35 (right), 12 (up), 27 (down) → 44 > 35, 12, 27 → supercell
Step 3: Check 31 (middle right): neighbors 29 (left), 18 (up), 20 (down) → 31 > 29, 18, 20 → supercell
Step 4: Check 33 (bottom middle): neighbors 27 (left), 20 (right), 29 (up) → 33 > 27, 20, 29 → supercell
Answer: Supercells are 35, 44, 31, and 33
40
Total Questions
100
Total Points
~45
Minutes