Question

6) Verify the property a×(b+c)=a×b+a×c by taking
a=-13/4 , b=5/2 , c= -7/6​

Answer 1

Answer:

a =13/4. , b) =5/2. , c=7/6.

Answer 2

What to do?

• Verify the property a × (b + c) = a × b + a × c by taking a = -13/4, b = 5/2 and c = -7/6.

Solution :-

• This is distributive property. We have to show that :-

$\sf \dfrac{ - 13}{ \: \: \: \: 4} \times \left(\dfrac{5}{2} + \dfrac{ - 7}{ \: \: \: 6} \right) = \dfrac{ - 13}{ \: \: \: \: 4} \times \dfrac{5}{2} + \dfrac{ - 13}{ \: \: \: \: 4} \times \dfrac{ - 7}{ \: \: \: 6}$

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LHS

$:\longmapsto\tt \dfrac{ - 13}{ \: \: \: \: 4} \times \left( \dfrac{5}{2} + \dfrac{ - 7}{ \: \: \: 6} \right)$

$:\longmapsto\tt \dfrac{ - 13}{ \: \: \: \: 4} \times \left(\dfrac{(5 \times 3) + ( - 7 \times 1)}{6} \right)$

$:\longmapsto \tt\dfrac{ - 13}{ \: \: \: \: 4} \times \left(\dfrac{15 - 7}{6} \right)$

$:\longmapsto\tt\dfrac{ - 13}{ \: \: \: \: 4} \times \dfrac{8}{6}$

Cancelling the numbers,

$:\longmapsto\tt \dfrac{ - 13}{ \: \: \: \: \: 1} \times \dfrac{1}{3}$

$:\longmapsto\tt\dfrac{ - 13}{ \: \: \: \: 3}$

RHS

$:\longmapsto\tt \dfrac{ - 13}{ \: \: \: \: 4} \times \dfrac{5}{2} + \dfrac{ - 13}{ \: \: \: \: 4} \times \dfrac{ - 7}{ \: \: 6}$

$:\longmapsto \tt\dfrac{ - 65}{ \: \: \: \: \: 8} + \dfrac{91}{24}$

$:\longmapsto\tt \dfrac{ (- 65 \times 3) + (91 \times 1)}{24}$

$:\longmapsto\tt\dfrac{ - 195 +91 }{24}$

$:\longmapsto \tt\dfrac{ - 104}{ \: \: \: \: \: 24}$

Cancelling the numbers,

$:\longmapsto \tt\dfrac{ - 13}{ \: \: \: \: 3}$

LHS = RHS.

Hence verified!

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