Question

Plz solve me this maths equation​

Answer 1

What to do?

• Verify that p × (q + r) = p × q + p × r by taking p = -3/5, q = 1/2 and r = -7/9.

Solution :-

• We have to show that :-

$\sf \dfrac{ - 3}{ \: \: \: 5} \times \left( \dfrac{1}{2} + \dfrac{ - 7}{ \: \: \: 9} \right) = \dfrac{ - 3}{ \: \: \: 5} \times \dfrac{1}{2} + \dfrac{ - 3}{ \: \: \: 5} \times \dfrac{ - 7}{ \: \: \: 9}$

LHS

$\implies\tt \dfrac{ - 3}{ \: \: \: 5} \times \bigg(\dfrac{1}{2} + \dfrac{ - 7}{ \: \: \: 9} \bigg)$

$\implies \tt\dfrac{ - 3}{ \: \: \: 5} \times \bigg( \dfrac{(1 \times 9) + ( - 7 \times 2)}{18} \bigg)$

$\implies\tt \dfrac{ - 3}{ \: \: \: 5} \times \bigg(\dfrac{9 - 14}{18} \bigg)$

$\implies \tt\dfrac{ - 3}{ \: \: \: 5} \times \dfrac{ - 5}{18}$

Cancelling the numbers,

$\implies\tt \dfrac{ - 1}{ \: \: \: 1} \times \dfrac{ - 1}{ \: \: \: 6}$

$\implies \tt\dfrac{1}{6}$

RHS

$\implies \tt\dfrac{ - 3}{ \: \: \: 5} \times \dfrac{1}{2} + \dfrac{ - 3}{ \: \: \: 5} \times \dfrac{ - 7}{ \: \: \: 9}$

$\implies \tt\dfrac{ - 3}{ \: 10} + \dfrac{21}{45}$

Reducing 21/45 to it's simplest form,

$\implies \tt\dfrac{ - 3}{ \: 10} + \dfrac{7}{15}$

$\implies \tt\dfrac{( - 3 \times 3) + (7 \times 2)}{30}$

$\implies \tt \dfrac{ - 9 + 14}{30}$

$\implies\tt \dfrac{5}{ 30}$

Reducing 5/30 to it's simplest form,

$\implies\tt\dfrac{1}{6}$

LHS = RHS.

Hence verified!!

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