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Mathematics

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

Whole Numbers: introduction, properties, successors/predecessors, and patterns
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 Whole numbers include zero.
1 pt
True
False
Answer: True
2.
True / False In this chapter, natural numbers do not include zero.
1 pt
True
False
Answer: True
3.
True / False Whole numbers are closed under addition and multiplication.
1 pt
True
False
Answer: True
4.
True / False Whole numbers are commutative under subtraction.
1 pt
True
False
Answer: False
5.
True / False Whole numbers are commutative under division.
1 pt
True
False
Answer: False
6.
True / False The additive identity for whole numbers is 1.
1 pt
True
False
Answer: False
7.
True / False The multiplicative identity for whole numbers is 1.
1 pt
True
False
Answer: True
8.
True / False 13 + 8 = 8 + 13.
1 pt
True
False
Answer: True
9.
True / False 13 × 0 = 1.
1 pt
True
False
Answer: False
10.
True / False The successor of the smallest whole number is 1.
1 pt
True
False
Answer: True
11.
Multiple Choice How many whole numbers are smaller than 8?
2 pts
A. 6
B. 7
C. 8
D. 9
Answer: C. 8
12.
Multiple Choice The additive identity of whole numbers is:
2 pts
A. 1
B. 0
C. 2
D. 3
Answer: B. 0
13.
Multiple Choice Which number is a power of both 2 and 3?
2 pts
A. 1
B. 0
C. 2
D. 3
Answer: A. 1
14.
Multiple Choice The successor of the smallest whole number is:
2 pts
A. 0
B. 1
C. 2
D. 3
Answer: B. 1
15.
Multiple Choice Find the successor of 8,06,998.
2 pts
A. 8,07,000
B. 8,06,999
C. 8,06,998
D. 8,06,997
Answer: B. 8,06,999
16.
Multiple Choice Which property is illustrated by 291 × (125 × 8)?
2 pts
A. Associative property
B. Closure property
C. Commutative property
D. Distributive property
Answer: A. Associative property
17.
Multiple Choice Find the sum of the predecessors of 84,636 and 90,025.
2 pts
A. 1,74,662
B. 1,74,661
C. 1,74,669
D. 1,74,659
Answer: D. 1,74,659
18.
Multiple Choice Which pair represents square numbers?
2 pts
A. 2 × 2, 1 × 2
B. 2 × 2, 3 × 3
C. 1 × 3, 4 × 4
D. 2 × 3, 4 × 2
Answer: B. 2 × 2, 3 × 3
19.
Multiple Choice Which of the following is not a natural number (with natural numbers starting at 1)?
2 pts
A. 8 × 6 ÷ 2
B. 3 × 4 − 4 × 3
C. 20 + 24 − 2
D. 18 + 5 − 5
Answer: B. 3 × 4 − 4 × 3
20.
Multiple Choice Choose the correct use of the distributive property: 64 × 12 + 64 × 14 =
2 pts
A. 12 × (64 + 14)
B. 64 × (12 + 14)
C. 14 × (64 + 12)
D. 12 × (64 + 64)
Answer: B. 64 × (12 + 14)
21.
Fill in the Blank The smallest whole number is _____.
2 pts
Answer: 0
22.
Fill in the Blank The successor of 0 is _____.
2 pts
Answer: 1
23.
Fill in the Blank The predecessor of 2,997 is _____.
2 pts
Answer: 2,996
24.
Fill in the Blank The successor of 8,06,998 is _____.
2 pts
Answer: 8,06,999
25.
Fill in the Blank The additive identity for whole numbers is _____.
2 pts
Answer: 0
26.
Fill in the Blank The multiplicative identity for whole numbers is _____.
2 pts
Answer: 1
27.
Fill in the Blank Writing 102 × 6 as (100 + 2) × 6 uses the _____ property.
2 pts
Answer: distributive
28.
Fill in the Blank The equality 2 + 4 = 4 + 2 shows the _____ property of addition.
2 pts
Answer: commutative
29.
Fill in the Blank 291 × (125 × 8) = (291 × 125) × 8 illustrates the _____ property of multiplication.
2 pts
Answer: associative
30.
Fill in the Blank Numbers used for counting (1, 2, 3, ...) are called _____ numbers.
2 pts
Answer: natural
31.
Word Problem Amal supplies 15 litres of milk daily at ₹30 per litre. How much does he earn in a week? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Daily earning = 15 × 30 = 450
Step 2: Weekly earning = 450 × 7 = 3,150
Answer: ₹3,150
32.
Word Problem 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?
5 pts
Working:
Answer:
Worked Solution:
Step 1: Days in June = 30
Step 2: Total expense = 150 × 30 = 4,500
Answer: ₹4,500
33.
Word Problem 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).
5 pts
Working:
Answer:
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 Find the product of the greatest 3-digit number and the greatest 2-digit number using a suitable property.
5 pts
Working:
Answer:
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 Evaluate 64 × 12 + 64 × 14 using the distributive property.
5 pts
Working:
Answer:
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 Find the sum by grouping: 703 + 768 + 297 + 322.
5 pts
Working:
Answer:
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 Verify the property (a × b) × c = (b × a) × c by taking a = 1, b = 3, c = 2. Show both sides.
5 pts
Working:
Answer:
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 Find the sum of the predecessors of 84,636 and 90,025.
5 pts
Working:
Answer:
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 How many whole numbers are smaller than 8? Show how you count them.
5 pts
Working:
Answer:
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 Raj bought 119 pieces of a fabric for ₹3,567 each. He returned 19 pieces for a full refund. What is his net spending?
5 pts
Working:
Answer:
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
40
Total Questions
100
Total Points
~35
Minutes