Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the difference between the smallest 4-digit whole number and the largest 3-digit whole number.
Correct! 1000 - 999 = 1.
(2) Write the smallest whole number divisible by both 6 and 9.
Perfect! LCM of 6 and 9 = 18 (excluding 0).
(3) Write the Roman numeral for 75.
Excellent! LXXV = 50 + 20 + 5 = 75.
(4) Write the sum of the place values of 7 in 7,072.
Great! 7,000 + 70 = 7,070.
(5) Which whole number is neither prime nor composite?
Correct! 1 is neither prime nor composite by definition.
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) Find the sum of the first 15 whole numbers.
Perfect! Using formula:
(2) Verify the commutative property of multiplication for 16 and 25. Product =
(3) Write the first 8 multiples of 12 and identify the common multiples of 6 and 12 from them.
First 8 multiples of 12:
Common multiples of 6 and 12:
(4) A number is divisible by both 2 and 3. Write the smallest such whole number greater than 20.
Excellent! 24 is the smallest number > 20 divisible by both 2 and 3.
(5) A basket has 1,248 apples packed equally into 12 boxes. How many apples are in each box?
Perfect! Each box contains 104 apples.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) Write and verify the distributive property of multiplication over subtraction for 15, 8, and 3.
(2) The product of two whole numbers is 5,040. If one number is 48, find the other number.
Excellent! The other number is 105.
(3) Arrange the first 10 whole numbers in a table showing their multiplication with 9.
Multiplication Table of 9:
| Number | × 9 | Result |
|---|---|---|
| 0 | × 9 | |
| 1 | × 9 | |
| 2 | × 9 | |
| 3 | × 9 | |
| 4 | × 9 | |
| 5 | × 9 | |
| 6 | × 9 | |
| 7 | × 9 | |
| 8 | × 9 | |
| 9 | × 9 |
(4) A school has 1,260 students. They are to be divided equally into groups of 15. Find the number of groups.
Perfect! There will be 84 groups.
(5) If the cost of 125 chairs is ₹ 75,000, find the cost of each chair and the cost of 150 such chairs.
Excellent! Cost of each chair = ₹ 600, Cost of 150 chairs = ₹ 90,000.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The sum of the first 20 whole numbers is:
(a) 200 (b) 210 (c) 190 (d) 220
Correct! Sum = 0+1+2+...+19 = 190.
(2) The smallest whole number divisible by 15 is:
(a) 0 (b) 15 (c) 30 (d) 45
Correct! 0 is divisible by every non-zero number.
(3) Which of the following is divisible by 11?
(a) 1,232 (b) 1,233 (c) 1,234 (d) 1,235
Correct! Using divisibility rule for 11: (1+3)-(2+2) = 0, divisible by 11.
(4) In Roman numerals, C stands for:
(a) 10 (b) 50 (c) 100 (d) 500
Correct! C represents 100 in Roman numerals.
(5) The LCM of 8 and 12 is:
(a) 24 (b) 48 (c) 36 (d) 12
Correct! LCM of 8 and 12 = 24.
(6) The HCF of 24 and 36 is:
(a) 6 (b) 8 (c) 12 (d) 18
Correct! HCF of 24 and 36 = 12.
(7) Which property is shown by: 7 × (4 + 5) = (7 × 4) + (7 × 5)?
(a) Commutative (b) Distributive (c) Associative (d) Identity
Correct! This shows distributive property of multiplication over addition.
(8) The largest 4-digit number divisible by 25 is:
(a) 9,975 (b) 9,950 (c) 9,900 (d) 9,999
Correct! Numbers divisible by 25 end in 00, 25, 50, or 75.
(9) Which of these is a multiple of both 4 and 6?
(a) 18 (b) 20 (c) 24 (d) 28
Correct! 24 is divisible by both 4 and 6 (LCM = 12, and 24 is a multiple of 12).
(10) If a × 1 = a for any whole number a, the property used is:
(a) Additive Identity (b) Multiplicative Identity (c) Associative Property (d) Distributive Property
Correct! 1 is the multiplicative identity element.
Complex Whole Number Properties
Determine whether these statements are True or False:
Whole Numbers - Hard Quiz
🎉 Outstanding Mastery! Advanced Whole Number Skills Achieved:
You have successfully conquered the "Whole Numbers (Hard)" worksheet and mastered:
(1) Advanced Arithmetic Operations: Computing complex sums, products, and divisions with large whole numbers
(2) LCM and HCF Calculations: Finding least common multiples and highest common factors using systematic methods
(3) Complex Number Properties: Understanding and applying distributive property over both addition and subtraction
(4) Divisibility Rules: Applying advanced rules for numbers like 11, along with basic rules for 2, 3, 5, and 15
(5) Roman Numeral System: Converting larger numbers to Roman numerals and understanding their structure
(6) Place Value Mastery: Calculating sums of place values for repeated digits in multi-digit numbers
(7) Prime and Composite Classification: Identifying special cases like 1 (neither prime nor composite)
(8) Mathematical Formulas: Using formulas for sum of consecutive numbers and verification techniques
(9) Real-world Problem Solving: Tackling complex word problems involving grouping, division, and cost calculations
(10) Pattern Recognition: Identifying multiples, common multiples, and relationships between numbers
(11) Mathematical Verification: Proving properties through numerical examples and systematic checking
(12) Table Construction: Organizing multiplication patterns and identifying mathematical relationships
(13) Advanced Property Applications: Demonstrating commutative, associative, distributive, and identity properties
(14) Multi-step Problem Solving: Breaking down complex problems into manageable computational steps
Exceptional achievement! You've mastered advanced whole number concepts with mathematical rigor!