NCERT Class 6 Solutions: Whole Numbers (Chapter 2) Exercise 2.2–Part 2

Q-4 Find the product using suitable properties:

  1. 738×103

  2. 854×102

  3. 258×1008

  4. 1005×168

Solution:

Understanding distributive property of multiplication over addition

Distributing Multiplication Over Addition

Understanding distributive property of multiplication over addition

Distributive property of multiplication over addition

Distributive Property of Multiplication Over Addition

Distributive property of multiplication over addition

  1. 738×103

    =738×103=738×(100+3)

    =738×100+738×3 (Distributive property of multiplication over addition)

    =73800+2214

    =76,014

  2. 854×102

    854×102=854×(100+2)

    =854×100+854×2 (Distributive property of multiplication over addition)

    =85400+1708

    =87,108

  3. 258×1008

    258×1008=258×(1000+8)

    =258×1000+258×8 (Distributive property of multiplication over addition)

    =258000+2064

    =2,60,064

  4. 1005×168

    1005×168=(1000+5)×168

    =1000×168+5×168 (Distributive property of multiplication over addition)

    =168000+840

    =1,68,840

Q-5 A taxi driver filled his car petrol tank with 40 liters of petrol on Monday. The next day, he filled the tank with 50 liters of petrol. If the petrol costs Rs 44 per liter, how much did he spend in all on petrol?

Solution:

Given the distributive law of multiplication over addition then simplify the expression

Given the Distributive Law of Multiplication Over Addition

Given the distributive law of multiplication over addition then simplify the expression

PetrolpurchasedonMonday=40liters

Costof1lofpetrol=Rs.44 so cost of 40 liters of petrol = 44×40

Petrolpurchasedonnextday=50liters

Costof1lofpetrol=Rs.44 so cost of 50 liters of petrol = 44×50

Totalcostofpetrol=(44×40+44×50)=44×(40+50) (Using distributive property of multiplication over addition)

= 90×44

= 3960Rs.

Q-6 A vendor supplies 32 liters of milk to a hotel in the morning and 68 liters of milk in the evening. If the milk costs Rs. 15 per liter, how much money is due to the vendor per day?

Solution:

Milksuppliedinmorning=32liters

Costof1lofmilk=Rs.15 so cost of 32 liters of petrol = 32×15

Milksuppliedinmorning=68liters

Costof1lofmilk=Rs.15 so cost of 68 liters of petrol = 68×15

Totalcostofpetrol=(32×15+68×15)=15×(32+68) (Using distributive property of multiplication over addition)

= 15×100

= 1500Rs.

Therefore, Rs. 1500 is due to the vendor per day.

Q-7 Match the following:

Given the match following of diffrent properties
Given the match following of diffrent properties and match the correctly
  1. 425×136=425×(6+30+100)

  1. Commutativity under multiplication

  • 2×48×50=2×50×49

  • Commutativity under addition

  • 80+2005+20=80+20+2005

  • Distibutivity multiplication under addition

Distributive, associative and commutative properties of additiona and multiplication illustrated with examples.

Distributive, Associative and Commutative Properties

Distributive, associative and commutative properties of additiona and multiplication illustrated with examples.

Understand the above properties, carefully note the difference between commutativity and associativity.

Solution:

  1. 425×136=425×(6+30+100)

  • We see that the number 136 is rewritten as 6+30+100

  • It is a distributive property of multiplication over addition (c)

Distributive property of multiplication over addition of whole numbers

Distributive Property of Multiplication Over Addition

Distributive property of multiplication over addition of whole numbers

  1. 2×(48×50)=2×(50×48)

    • We see that the numbers are rearranged under the multiplication operation.

    • It is a commutativity under multiplication (associativity on the other hand would be 2×(48×50)=(2×50)×48)

    Commutativity under multiplication with butterflies

    Commutativity Under Multiplication

    Commutativity under multiplication with butterflies

  2. 80+(2005+20)=80+(20+2005)

  • The numbers are rearranged under the addition operation.

  • It is a commutative under addition (associativity on the other hand would be 80+(2005+20)=(80+20)+2005)

Commutativity under addition with apples

Commutativity Under Addition

Commutativity under addition with apples

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