Expressing the number that is one less than 100 in words. 8.2, 4, 6. Down: Successor of 10378695. 3. Place of International System of numeration after Ones and Tens. Greatest one-digit number in words: 7. Number of zeroes in one thousand. Q2. Write the HCF of two consecutive numbers. Q3. Write all prime numbers less than 15. Q4. Find the common multiples of 3 and 4. Q6. Write all the factors of 36. Q7. Find the LCM of 27 and 63. Q8. Find the product by the distributivity property: 168 x 102. Q9. How many whole numbers are there between 12 and 862? Q10. Write the largest 6-digit number having two different digits. Q11. Round off to the nearest hundreds: 17,297. Q12. Write 73403 in expanded form. Q13. Name the properties used in the following operations
The Correct Answer and Explanation is:
- Expressing the number that is one less than 100 in words: Ninety-nine
- Down: Successor of 10378695: 10378696
- Place of International System of numeration after Ones and Tens: Hundreds
- Greatest one-digit number in words: Nine
- Number of zeroes in one thousand: Three
- Q2. HCF of two consecutive numbers: 1
- Q3. Prime numbers less than 15: 2, 3, 5, 7, 11, 13
- Q4. Common multiples of 3 and 4 (first five): 12, 24, 36, 48, 60
- Q6. All factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Q7. LCM of 27 and 63: 189
- Q8. 168 × 102 using distributivity:
168 × (100 + 2) = (168 × 100) + (168 × 2) = 16800 + 336 = 17136 - Q9. Whole numbers between 12 and 862: 862 − 12 − 1 = 849
- Q10. Largest 6-digit number with two different digits: 999990
- Q11. Round 17,297 to the nearest hundreds: 17,300
- Q12. 73403 in expanded form:
70,000 + 3,000 + 400 + 0 + 3
Q13. Name the properties used in the following operations:
- 168 × (100 + 2) = 168 × 100 + 168 × 2
Property used: Distributive property of multiplication over addition
Explanation
This set of questions explores fundamental mathematical concepts that form the building blocks for more advanced problem-solving. Understanding place value is critical in expressing numbers in words (e.g., 99 as ninety-nine), identifying positions like hundreds in the International System, and performing rounding operations (e.g., 17,297 rounded to 17,300).
The successor of a number is simply one more than the number itself, while prime numbers are those with exactly two distinct factors: 1 and the number itself (like 2, 3, 5, etc.). Prime numbers play a key role in topics like factorization and cryptography.
The HCF (Highest Common Factor) of two consecutive numbers is always 1, since they do not share any common divisors except 1. In contrast, the LCM (Least Common Multiple) finds the smallest number that is divisible by both numbers, useful in synchronizing cycles or patterns.
The distributive property (e.g., 168 × 102 = 168 × (100 + 2)) simplifies multiplication and helps in mental math. It’s a vital algebraic tool for simplifying expressions and solving equations.
Factors and multiples reveal number relationships: factors divide a number exactly, while multiples are obtained by multiplying the number by integers. Identifying common multiples (like of 3 and 4) helps with least common multiple (LCM) problems.
Understanding how to count whole numbers between a range builds number sense, while tasks like expanded form (e.g., 73403 = 70000 + 3000 + 400 + 3) reinforce place value comprehension.
Lastly, constructing the largest number with certain digit constraints (like 999990 with two digits) encourages creative thinking in number composition.
These foundational skills develop arithmetic fluency and analytical reasoning, essential for higher-level math and real-world problem-solving.
