Solved Examples on Properties of Whole Numbers
1. Fill in the following blanks with suitable answers.
i. 120 × (273 + 40) = _____ + (120 × 40)
ii. 89 × 12 = 12 × (80 + ____ )
iii. 60 × 204 = (60 × 200) + (60 × ____ )
a) i. 120 x 273, ii. 9, iii. 4
b) i. 273 x 273, ii. 9, iii. 4
c) i. 120 x 120, ii. 9, iii. 4
d) i. 150 x 273, ii. 9, iii. 4
Answer: a) i. 120 x 273, ii. 9, iii. 4
Explanation: i. 120 × (273 + 40) = 120 x 273 + ( 120 × 40 )
ii. 89 × 12 = 12 × (80 + 9)
iii. 60 × 204 = (60 × 200) + (60 × 4)
2. Solve 14 × (3 + 7) using the distributive property.
a) 100
b) 120
c) 130
d) 140
Answer: d) 140
Explanation: The distributive property of multiplication over the addition of whole numbers is: a × (b + c) = (a × b) + (a × c)
So, 14 × (3 + 7) = (14 × 3) + (14 × 7)
= 42 + 98
= 140
Hence, the value of 14 × (3 + 7) is 140.
3. Jacqueline distributes 32 boxes of sweets on her birthday in her class. Each box comprises 10 candies and 2 small chocolate balls. Calculate the number of sweets in the 32 boxes.
a) 300
b) 328
c) 362
d) 384
Answer: d) 384
Explanation: Number of boxes of sweets: 32
Number of candies in each box = 10
Number of small chocolate balls in each box = 2
Total number of sweets : 32 × ( 10 + 2 ) = (32 × 10) + (32 × 2) = 320 + 64 = 384
4. What property can be applied to the following expression? (8 + 4) + 11 = 8 + (4 + 11)
a) Associative property
b) Closure property
c) Commutative property
d) Distributive property
Answer: a) Associative property
Explanation: The rule for Associative Property of Addition is (a + b) + c = a + (b + c)
Expression given in the question is: (8 + 4) + 11 = 8 + (4 + 11)
Hence, the property is associative property.
5. Find the following product using the distributive property of whole numbers: 82 × 45
a) 3200
b) 3408
c) 3690
d) 3720
Answer: c) 3690
Explanation: By using the distributive property, we can write the given product as follows: 82 × 45 = (80 + 2) × (40 + 5)
= 80 × 40 + 80 × 5 + 2 × 40 + 2 × 5
= 3200 + 400 + 80 + 10
= 3690
Therefore, 82 × 45 = 3690.
Practice Questions on Properties of Whole Numbers
1. Samuel filled his truck’s tank with 20 gallons of fuel. He filled the tank with 40 gallons of fuel the next day. How much did he spend on fuel if it costs $4 per gallon?
a) $240
b) $320
c) $335
d) $340
Answer: a) $240
2. Pola got an opportunity to work at a client’s place and his stay and food are taken care of by his company, he lives in a seven-star hotel provided by his company for seven days. Charges are $55 for dinner and $45 for lunch. How much money does it cost for dinner and lunch together for seven days?
a) $200
b) $500
c) $700
d) $1200
Answer: c) $700
3. 3 cartons have 3072 crayons altogether. Each carton has an equal number of packets. Each packet contains 8 crayons. Find the number of packets in each carton.
a) 100
b) 128
c) 132
d) 143
Answer: b) 128
4. Which identity is used to add the numbers 194, 127 and 873?
a) Commutative property
b) Associative property
c) Distributive property
d) Closure property
Answer: b) Associative property
5. Solve 20 × (928 + 857).
a) 35700
b) 37500
c) 31500
d) 35500
Answer: a) 35700
6. What number should replace the value of Z in the following expression below, (11 × 72) + (11 × 20) = (72 + 20) × Z ?
a) 9
b) 10
c) 11
d) 12
Answer: c) 11
7. Andrew wants to divide his 40 acres of land among his five daughters, How many acres of land did each daughter get?
a) 6
b) 8
c) 5
d) 4
Answer: b) 8
8. Sam is a baker, He is good at baking cupcakes, He bakes 32 cupcakes and divides them equally into 4 packets. How many cupcakes are there in each packet?
a) 12
b) 10
c) 8
d) 4
Answer: c) 8
9. What is the identity element for the addition of whole numbers?
a) 0
b) 1
c) 2
d) -1
Answer: a) 0
10. John has 9 marbles and he gives 3 marbles to each of his 2 friends. How many marbles does John have left?
a) 1
b) 3
c) 4
d) 6
Answer: b) 3
