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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
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