Whole Numbers: Properties, Operations, and Patterns — Grade 6 Review

1. True / False (1 pts)

Whole numbers include zero.

✓ Answer

True

2. True / False (1 pts)

In this chapter, natural numbers do not include zero.

✓ Answer

True

3. True / False (1 pts)

Whole numbers are closed under addition and multiplication.

✓ Answer

True

4. True / False (1 pts)

Whole numbers are commutative under subtraction.

✓ Answer

False

5. True / False (1 pts)

Whole numbers are commutative under division.

✓ Answer

False

6. True / False (1 pts)

The additive identity for whole numbers is 1.

✓ Answer

False

7. True / False (1 pts)

The multiplicative identity for whole numbers is 1.

✓ Answer

True

8. True / False (1 pts)

13 + 8 = 8 + 13.

✓ Answer

True

9. True / False (1 pts)

13 × 0 = 1.

✓ Answer

False

10. True / False (1 pts)

The successor of the smallest whole number is 1.

✓ Answer

True

11. Multiple Choice (2 pts)

How many whole numbers are smaller than 8?

✓ Answer

C. 8

12. Multiple Choice (2 pts)

The additive identity of whole numbers is:

✓ Answer

B. 0

13. Multiple Choice (2 pts)

Which number is a power of both 2 and 3?

✓ Answer

A. 1

14. Multiple Choice (2 pts)

The successor of the smallest whole number is:

✓ Answer

B. 1

15. Multiple Choice (2 pts)

Find the successor of 8,06,998.

✓ Answer

B. 8,06,999

16. Multiple Choice (2 pts)

Which property is illustrated by 291 × (125 × 8)?

✓ Answer

A. Associative property

17. Multiple Choice (2 pts)

Find the sum of the predecessors of 84,636 and 90,025.

✓ Answer

D. 1,74,659

18. Multiple Choice (2 pts)

Which pair represents square numbers?

✓ Answer

B. 2 × 2, 3 × 3

19. Multiple Choice (2 pts)

Which of the following is not a natural number (with natural numbers starting at 1)?

✓ Answer

B. 3 × 4 − 4 × 3

20. Multiple Choice (2 pts)

Choose the correct use of the distributive property: 64 × 12 + 64 × 14 =

✓ Answer

B. 64 × (12 + 14)

21. Fill in the Blank (2 pts)

The smallest whole number is _____.

✓ Answer

0

22. Fill in the Blank (2 pts)

The successor of 0 is _____.

✓ Answer

1

23. Fill in the Blank (2 pts)

The predecessor of 2,997 is _____.

✓ Answer

2,996

24. Fill in the Blank (2 pts)

The successor of 8,06,998 is _____.

✓ Answer

8,06,999

25. Fill in the Blank (2 pts)

The additive identity for whole numbers is _____.

✓ Answer

0

26. Fill in the Blank (2 pts)

The multiplicative identity for whole numbers is _____.

✓ Answer

1

27. Fill in the Blank (2 pts)

Writing 102 × 6 as (100 + 2) × 6 uses the _____ property.

✓ Answer

distributive

28. Fill in the Blank (2 pts)

The equality 2 + 4 = 4 + 2 shows the _____ property of addition.

✓ Answer

commutative

29. Fill in the Blank (2 pts)

291 × (125 × 8) = (291 × 125) × 8 illustrates the _____ property of multiplication.

✓ Answer

associative

30. Fill in the Blank (2 pts)

Numbers used for counting (1, 2, 3, ...) are called _____ numbers.

✓ Answer

natural

31. Word Problem (5 pts)

Amal supplies 15 litres of milk daily at ₹30 per litre. How much does he earn in a week? Show your working.

✎ Worked Solution

Step 1: Daily earning = 15 × 30 = 450

Step 2: Weekly earning = 450 × 7 = 3,150

Answer: ₹3,150

32. Word Problem (5 pts)

Raman incurs a daily travel expense of ₹150 going to and from his office. How much does he spend on travel in the month of June?

✎ Worked Solution

Step 1: Days in June = 30

Step 2: Total expense = 150 × 30 = 4,500

Answer: ₹4,500

33. Word Problem (5 pts)

Sonu goes to music class four days a week and Manu goes three days a week. Calculate the total number of days they attend the class in a year (52 weeks).

✎ Worked Solution

Step 1: Sonu's days per year = 4 × 52 = 208

Step 2: Manu's days per year = 3 × 52 = 156

Step 3: Total days = 208 + 156 = 364

Answer: 364 days

34. Word Problem (5 pts)

Find the product of the greatest 3-digit number and the greatest 2-digit number using a suitable property.

✎ Worked Solution

Step 1: Greatest 3-digit = 999; Greatest 2-digit = 99

Step 2: 999 × 99 = 999 × (100 − 1)

Step 3: = 99,900 − 999 = 98,901

Answer: 98,901

35. Word Problem (5 pts)

Evaluate 64 × 12 + 64 × 14 using the distributive property.

✎ Worked Solution

Step 1: 64 × 12 + 64 × 14 = 64 × (12 + 14)

Step 2: 12 + 14 = 26

Step 3: 64 × 26 = 64 × 20 + 64 × 6 = 1,280 + 384 = 1,664

Answer: 1,664

36. Word Problem (5 pts)

Find the sum by grouping: 703 + 768 + 297 + 322.

✎ Worked Solution

Step 1: Group as (703 + 297) + (768 + 322)

Step 2: 703 + 297 = 1,000; 768 + 322 = 1,090

Step 3: 1,000 + 1,090 = 2,090

Answer: 2,090

37. Word Problem (5 pts)

Verify the property (a × b) × c = (b × a) × c by taking a = 1, b = 3, c = 2. Show both sides.

✎ Worked Solution

Step 1: (1 × 3) × 2 = 3 × 2 = 6

Step 2: (3 × 1) × 2 = 3 × 2 = 6

Step 3: Both sides are equal

Answer: Property holds (both sides equal 6)

38. Word Problem (5 pts)

Find the sum of the predecessors of 84,636 and 90,025.

✎ Worked Solution

Step 1: Predecessor of 84,636 = 84,635; Predecessor of 90,025 = 90,024

Step 2: Sum = 84,635 + 90,024

Step 3: 84,635 + 90,024 = 1,74,659

Answer: 1,74,659

39. Word Problem (5 pts)

How many whole numbers are smaller than 8? Show how you count them.

✎ Worked Solution

Step 1: Whole numbers from 0 up to 7 are: 0, 1, 2, 3, 4, 5, 6, 7

Step 2: Count them = 8 numbers

Answer: 8

40. Word Problem (5 pts)

Raj bought 119 pieces of a fabric for ₹3,567 each. He returned 19 pieces for a full refund. What is his net spending?

✎ Worked Solution

Step 1: Net pieces kept = 119 − 19 = 100

Step 2: Net amount = 3,567 × 100

Step 3: 3,567 × 100 = 356,700

Answer: ₹356,700