Question

Verify distributive property of multiplication over addition for the rational numbers a= -2/3 ,b= 5/6 , c= 7/9 .

Answer 1

$\underline{ \pink{ Distributive \: law\:of \: Multiplication \: over \: addition : }}$

$\boxed{\blue{ a(b+c) = a \times b + a \times c }}$

$Here, given \: a = \frac{ -2}{3} , b = \frac{5}{6} \\and \: c = \frac{ 7}{9}$

$\red{ LHS = a( b +c ) } \\= \frac{ -2}{3} \Big( \frac{5}{6} + \frac{ 7}{9} \Big) \\= \frac{-2}{3} \Big( \frac{15+14}{18} \Big) \\= \frac{-2}{3} \times \frac{29}{18} \\= \frac{-29}{27} \: --(1)$

$\red{ RHS = a\times b +a \times c } \\= = \Big(\frac{ -2}{3} \Big) \times \frac{5}{6} +\Big( \frac{-2}{3} \Big)\times \frac{ 7}{9} \\= \frac{-5}{9} - \frac{14}{27} \\= \frac{-15-14}{27} \\= \frac{-29}{27} \: --(2)$

$\green { LHS = RHS }\: [ From \: (1) \: and \: (2) ]$

Therefore.,

$\blue{\frac{ -2}{3} \Big( \frac{5}{6} + \frac{ 7}{9} \Big) = \Big(\frac{ -2}{3} \Big) \times \frac{5}{6} +\Big( \frac{-2}{3} \Big)\times \frac{ 7}{9} }$

•••♪