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Verify the following properties for the given values of a, b, c. $a=-3, b=1$ and $c=-4$.Property 1: $a\div (b+c) ≠(a÷b) +c$
Property 2: $a\times (b+c) =(a\times b)+(a\times c)$
Property 3: $a\times (b-c)=(a\times b) -(a\times c)$
Given :
$a=-3, b=1$ and $c=-4$.
To do :
We have to verify the following properties, for the given values of a, b, c.
Property 1: $a\div (b+c) ≠ (a÷b) +c$
Property 2: $a\times (b+c) =(a\times b)+(a\times c)$
Property 3: $a\times (b-c)=(a\times b) -(a\times c)$
Solution :
Property 1: $a\div (b+c) ≠ (a÷b) +c$
LHS
$a÷(b+c) = -3÷(1+(-4)) = -3÷(1-4) = -3÷-3 = \frac{-3}{-3} = 1$.
RHS
$(a÷b) +c = (-3÷1)+(-4) = (-3)-4 = -7$.
$LHS ≠ RHS$
Therefore,
$a÷(b+c) ≠(a÷b) +c$.
Hence verified.
Property 2: $a\times (b+c) =(a\times b)+(a\times c)$
LHS
$a\times (b+c) = (-3)\times (1+(-4))=(-3)\times (1-4) = (-3)\times (-3) = 9$
RHS
$(a\times b)+(a\times c) = (-3\times 1)+(-3\times -4)=(-3)+12 = 12-3 = 9$
$LHS = RHS$
Therefore,
$a\times (b+c) =(a\times b)+(a\times c)$.
Hence verified.
Property 3: $a\times (b-c)=(a\times b) -(a\times c)$
LHS
$a\times (b-c) = (-3) \times (1-(-4)) = (-3)\times (1+4)=(-3)\times 5 = -15$
RHS
$(a\times b) -(a\times c) = (-3\times 1)-(-3\times -4) = (-3)-(12) = -(3+12) = -15$
$LHS = RHS$
Therefore,
$a\times (b-c)=(a\times b) -(a\times c)$.
Hence verified.
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