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Mathematics

Playing with Numbers Worksheet

Operations, BODMAS, Multiples, Factors and Divisibility
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 The rabbit takes one step forward for each correct answer.
1 pt
True
False
Answer: True
2.
True / False The result of 4 × 100 + 7 × 10 + 3 is 473.
1 pt
True
False
Answer: True
3.
True / False According to the BODMAS rule, operations inside brackets are performed first.
1 pt
True
False
Answer: True
4.
True / False In a multi-operation problem, subtraction is always carried out first.
1 pt
True
False
Answer: False
5.
True / False The property LCM × HCF = Product of two numbers holds true for any pair of numbers.
1 pt
True
False
Answer: True
6.
True / False Prime factorization involves breaking down a number into its prime factors.
1 pt
True
False
Answer: True
7.
True / False A prime number has more than two distinct factors.
1 pt
True
False
Answer: False
8.
True / False Multiples of a number are obtained by repeatedly adding the number to itself.
1 pt
True
False
Answer: True
9.
True / False If a number is divisible by both 9 and 11, it is always divisible by 90.
1 pt
True
False
Answer: False
10.
True / False A perfect number is one that is equal to the sum of its proper divisors.
1 pt
True
False
Answer: True
11.
Multiple Choice What is 4 × 100 + 7 × 10 + 3?
2 pts
A. 473
B. 4730
C. 470
D. 4733
Answer: A. 473
12.
Multiple Choice What is 10 less than 10 times 51?
2 pts
A. 500
B. 510
C. 520
D. 490
Answer: A. 500
13.
Multiple Choice What is the simplified form of 5 × 10,000 + 9 × 10 + 1?
2 pts
A. 50091
B. 50100
C. 50090
D. 50081
Answer: A. 50091
14.
Multiple Choice According to the BODMAS rule, which operation should be performed first?
2 pts
A. Addition
B. Multiplication
C. Brackets
D. Subtraction
Answer: C. Brackets
15.
Multiple Choice The HCF of two coprime numbers is:
2 pts
A. 0
B. 1
C. The smaller number
D. The larger number
Answer: B. 1
16.
Multiple Choice In prime factorization, which number is considered the smallest prime?
2 pts
A. 1
B. 2
C. 4
D. 6
Answer: B. 2
17.
Multiple Choice Which of the following numbers is divisible by 3?
2 pts
A. 73
B. 54
C. 137
D. 277
Answer: B. 54
18.
Multiple Choice What does LCM stand for?
2 pts
A. Least Common Multiple
B. Lowest Common Measure
C. Largest Common Multiple
D. Least Common Factor
Answer: A. Least Common Multiple
19.
Multiple Choice What is the key concept behind the factor tree method?
2 pts
A. Division into prime factors
B. Multiplication only
C. Addition of factors
D. Subtraction of numbers
Answer: A. Division into prime factors
20.
Multiple Choice Which statement is true about prime numbers?
2 pts
A. All even numbers are prime
B. 2 is the only even prime number
C. 1 is a prime number
D. Prime numbers are divisible by 2
Answer: B. 2 is the only even prime number
21.
Fill in the Blank In the number 4 × 100 + 7 × 10 + 3, the digit in the tens place is _____ .
2 pts
Answer: 7
22.
Fill in the Blank The result of 10 times 51 minus 10 is _____ .
2 pts
Answer: 500
23.
Fill in the Blank The simplified expression for 5 × 10,000 + 9 × 10 + 1 is _____ .
2 pts
Answer: 50091
24.
Fill in the Blank According to the BODMAS rule, operations inside _____ are performed first.
2 pts
Answer: brackets
25.
Fill in the Blank The smallest factor of every number is _____ .
2 pts
Answer: 1
26.
Fill in the Blank Prime factorization breaks a number into its _____ factors.
2 pts
Answer: prime
27.
Fill in the Blank LCM stands for Least Common _____ .
2 pts
Answer: Multiple
28.
Fill in the Blank The property LCM × HCF = Product of two numbers shows the relation between _____.
2 pts
Answer: multiples and factors
29.
Fill in the Blank Divisibility by 3 is determined by the sum of the _____ of a number.
2 pts
Answer: digits
30.
Fill in the Blank A perfect number is one that is equal to the sum of its _____ divisors.
2 pts
Answer: proper
31.
Word Problem A rabbit hops forward each time a correct answer is given. If it takes 473 steps to reach a carrot, and each correct answer moves it 1 step, how many correct answers did it get? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Recognize each correct answer equals 1 step
Step 2: Total steps = 473
Answer: 473
32.
Word Problem Solve: 10 less than 10 times 51. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Calculate 10 × 51 = 510
Step 2: Subtract 10: 510 - 10
Answer: 500
33.
Word Problem Evaluate: 5 × 10,000 + 9 × 10 + 1 × 1. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Calculate 5 × 10,000 = 50000
Step 2: Calculate 9 × 10 = 90
Step 3: Add 50000 + 90 + 1
Answer: 50091
34.
Word Problem Calculate 36,000 + 400 - 100 + 10. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Add 36,000 + 400 = 36400
Step 2: Subtract 100: 36400 - 100 = 36300
Step 3: Add 10: 36300 + 10
Answer: 36310
35.
Word Problem Find the least common multiple (LCM) of 15 and 20. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factors: 15 = 3 × 5, 20 = 2² × 5
Step 2: LCM = 2² × 3 × 5
Answer: 60
36.
Word Problem Determine the highest common factor (HCF) of 36 and 60. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Prime factors: 36 = 2² × 3², 60 = 2² × 3 × 5
Step 2: HCF = 2² × 3
Answer: 12
37.
Word Problem A six-digit number has digits that sum to 27. Explain why this number is divisible by 9. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Sum of digits = 27
Step 2: Since 27 ÷ 9 = 3 exactly
Answer: The number is divisible by 9
38.
Word Problem In a colony with 62 blocks, a bus stops every 10th block and a van every 6th block. What is the first block where both vehicles stop? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find LCM of 6 and 10 = 30
Step 2: First common stop is block 30
Answer: 30
39.
Word Problem If the property LCM × HCF = Product of two numbers holds, and the LCM of two numbers is 60 while the HCF is 12, find the product of the two numbers. Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Multiply LCM and HCF: 60 × 12
Step 2: Compute the product
Answer: 720
40.
Word Problem Three water tankers have capacities of 5000, 8000, and 10,000 litres. What is the maximum capacity of a container that can measure all three tanks exactly? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Find HCF of 5000, 8000, and 10000
Step 2: HCF = 1000
Answer: 1000
40
Total Questions
100
Total Points
~35
Minutes