Question

solve the following using associate property
$( \frac{7}{8} + \frac{2}{5} ) + \frac{8}{3}$

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Answer 1

Question

solve the following using associate property

$( \frac{7}{8} + \frac{2}{5} ) + \frac{8}{3}$

Answer

$( \large \bf\frac{7}{8} + \frac{2}{5} ) + \frac{8}{3}$

Here,

Let a = $\bf\frac{7}{2}$

Let b = $\bf\frac{2}{5}$

And c = $\bf\frac{8}{3}$

According to associative property, it states that

(a+b)+c = a+(b+c)

LHS↓

$( \bf\frac{7}{8} + \frac{2}{5} ) + \frac{8}{3}$

$\mapsto\tt(\frac{7}{8} + \frac{2}{5}) + \frac{8}{3}$

$\mapsto\tt(\frac{(7 \times 5) + (2 \times 8)}{40} ) + \frac{8}{3}$

$\mapsto\tt(\frac{35 + 16}{40} ) + \frac{8}{3}$

$\mapsto\tt\frac{51}{40} + \frac{8}{3}$

$\mapsto\tt\frac{(51 \times 3) + (8 \times 40)}{120}$

$\mapsto\tt\frac{(153 + 320)}{120}$

$\mapsto\tt\frac{473}{120}$

RHS↓

$\bf\frac{7}{8} +( \frac{2}{5} + \frac{8}{3})$

$\mapsto \tt\frac{7}{8} +( \frac{2}{5} + \frac{8}{3})$

$\mapsto \tt\frac{7}{8} +( \frac{(2 \times 3) + (5 \times 8)}{15} )$

$\mapsto \tt\frac{7}{8} + (\frac{ 6 + 40}{15} )$

$\mapsto \tt\frac{7}{8} + \frac{46}{15}$

$\mapsto \tt\frac{(7 \times 15) + (46 \times 8)}{120}$

$\mapsto \tt\frac{105 + 368}{120}$

$\mapsto \tt\frac{473}{120}$

LHS = RHS

Hence verified!!