Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Q1. For each of the following values of a,b and c, where
(a) a = -20, b = -10, c = 5
(b) a = -40, b = 10, c = -5
Show that:
(i) a÷b ≠ b÷a
(ii) (a÷b)÷c ≠ a÷(b÷c)
(iii) a÷(b+c)≠(a÷b)+(a÷c)​

Sagot :

SalmonWorldTopper

Explanation:-

⟨a⟩

Given that

a = -20

b = -10

c = 5

⟨i⟩ LHS = a÷b

⇛ -20÷-10

⇛ -20/-10

⇛ 2

and

RHS = b÷a

⇛ -10÷-20

⇛ -10/-20

⇛ 1/2

LHS ≠ RHS

a÷b ≠ b÷a

⟨ii⟩

LHS = (a÷b)÷c

⇛ (-20÷-10)÷5

⇛ 2÷5

⇛ 2/5

RHS = a÷(b÷c)

⇛ -20÷(-10÷5)

⇛ -20÷-2

⇛ -20/-2

⇛ 10

LHS ≠ RHS

(a÷b)÷c ≠ a÷(b÷c)

⟨iii⟩ LHS = a÷(b+c)

⇛ -20÷(-10+5)

⇛ -20÷(-5)

⇛ -20/-5

⇛ 4

RHS = (a÷b)+(a÷c)

⇛ (-20÷-10)+(-20÷5)

⇛ 2+(-4)

⇛ 2-4

⇛ -2

LHS ≠ RHS

a÷(b+c) ≠ (a÷b)+(a÷c)

⟨b⟩.

Given that

a = -40

b = 10

c = -5

⟨i⟩ LHS = a÷b

⇛ -40÷1

⇛ -40/1

⇛-40

and

RHS = b÷a

⇛ 10÷-40

⇛ 10/-40

⇛ -1/4

LHS ≠ RHS

a÷b ≠ b÷a

⟨ii⟩.

LHS = (a÷b)÷c

⇛ (-40÷10)÷-5

⇛ -4÷-5

⇛ 4/5

RHS = a÷(b÷c)

⇛ -40÷(10÷-5)

⇛ -40÷-2

⇛ -40/-2

⇛ 20

LHS ≠ RHS

(a÷b)÷c ≠ a÷(b÷c)

⟨iii⟩ LHS = a÷(b+c)

⇛ -40÷(10-5)

⇛ -40÷(5)

⇛ -40/5

⇛ -8

RHS = (a÷b)+(a÷c)

⇛ (-40÷10)+(-40÷-5)

⇛ (-4)+8

⇛ 8-4

⇛ 4

LHS ≠ RHS

a÷(b+c) ≠ (a÷b)+(a÷c)

Conclusion :-

  1. Commutative property
  2. Associative Property
  3. Distributive Property does not hold in the set of integers under Division
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.