Playing With Numbers: Class 6 Mixed Practice

1. True / False (1 pts)

Zero is a whole number.

✓ Answer

True

2. True / False (1 pts)

In the set of whole numbers, 0 has a predecessor.

✓ Answer

False

3. True / False (1 pts)

Addition of whole numbers is commutative.

✓ Answer

True

4. True / False (1 pts)

Subtraction of whole numbers is associative.

✓ Answer

False

5. True / False (1 pts)

Whole numbers are closed under multiplication.

✓ Answer

True

6. True / False (1 pts)

In the Indian system, the number 12,34,567 is correctly grouped with commas.

✓ Answer

True

7. True / False (1 pts)

The number 1 is a prime number.

✓ Answer

False

8. True / False (1 pts)

Every even number is divisible by 4.

✓ Answer

False

9. True / False (1 pts)

999 rounded to the nearest thousand is 1000.

✓ Answer

True

10. True / False (1 pts)

A number is divisible by 3 if the sum of its digits is a multiple of 3.

✓ Answer

True

11. Multiple Choice (2 pts)

Which number is the greatest?

✓ Answer

D. 760

12. Multiple Choice (2 pts)

In 3,58,241 (Indian system), the place value of the digit 5 is:

✓ Answer

B. 50,000

13. Multiple Choice (2 pts)

Write 27,05,300 (Indian system) in the International system.

✓ Answer

B. 2,705,300

14. Multiple Choice (2 pts)

Round 46,372 to the nearest 1,000.

✓ Answer

B. 46,000

15. Multiple Choice (2 pts)

Evaluate: 18 − [6 + 2 × (7 − 4)]

✓ Answer

C. 6

16. Multiple Choice (2 pts)

Which is the correct Roman numeral for 90?

✓ Answer

C. XC

17. Multiple Choice (2 pts)

Which of the following is a prime number?

✓ Answer

B. 97

18. Multiple Choice (2 pts)

Which number is divisible by 9?

✓ Answer

A. 7,245

19. Multiple Choice (2 pts)

The HCF of 36 and 60 is:

✓ Answer

B. 12

20. Multiple Choice (2 pts)

How many 4-digit numbers exist?

✓ Answer

C. 9,000

21. Fill in the Blank (2 pts)

Zero is the smallest _____ number.

✓ Answer

whole

22. Fill in the Blank (2 pts)

The successor of 4,999 is _____.

✓ Answer

5000

23. Fill in the Blank (2 pts)

In the Indian system, 1,00,000 is called one _____.

✓ Answer

lakh

24. Fill in the Blank (2 pts)

The additive identity for whole numbers is _____.

✓ Answer

0

25. Fill in the Blank (2 pts)

300 + 20 + 5 in standard form is _____.

✓ Answer

325

26. Fill in the Blank (2 pts)

A number divisible by 2 and 5 is always divisible by _____.

✓ Answer

10

27. Fill in the Blank (2 pts)

The prime factorization of 84 is 2 × 2 × 3 × _____.

✓ Answer

7

28. Fill in the Blank (2 pts)

In Roman numerals, 40 is written as _____.

✓ Answer

XL

29. Fill in the Blank (2 pts)

The place value of 9 in 5,19,804 (Indian system) is _____.

✓ Answer

9000

30. Fill in the Blank (2 pts)

On a number line, moving 7 units left from 15 lands on _____.

✓ Answer

8

31. Word Problem (5 pts)

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.

✎ 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 (5 pts)

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.

✎ 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 (5 pts)

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.

✎ 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 (5 pts)

What is the least number that must be subtracted from 5,237 to make it divisible by 6? Show your working.

✎ 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 (5 pts)

Find the LCM of 48 and 180 using prime factorization. Show your working.

✎ 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 (5 pts)

A shop calculates a bill as (250 + 75) × 4 − 180. Find the final amount. Show your working.

✎ 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 (5 pts)

Convert the number 2,019 to Roman numerals. Show your working.

✎ 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 (5 pts)

Write 4,57,20,608 (Indian system) in the International system with commas. Show your working.

✎ 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 (5 pts)

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.

✎ 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 (5 pts)

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.

✎ 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