Question

verify the distributive property
aX(b+c)=(aXb) for the rational number
a=1/3. b=-1/2. c=4/7​

Answer 1

See the screenshot attached below

Answer 2

a × ( b + c ) = ( a × b ) + ( a × c)

$\frac{1}{3}$ × ( $\frac{-1}{2}$ + $\frac{4}{7}$ ) = ( $\frac{1}{3}$ × $\frac{-1}{2}$ ) + ( $\frac{1}{3}$ × $\frac{4}{7}$ )

First let us solve: LHS

LCM of 2 and 7 = 14

so,  $\frac{1}{3}$ × ( $\frac{-7}{14}$ + $\frac{8}{14}$ ) =  $\frac{1}{3}$ × $\frac{1}{14}$

$\frac{1}{3}$ × $\frac{1}{14}$ = $\frac{1}{42}$

Now, let us solve: RHS

( $\frac{1}{3}$ × $\frac{-1}{2}$ )

LCM of 3 and 2 = 6

( $\frac{2}{6}$ × $\frac{-3}{6}$ ) =  $\frac{-6}{36}$

AND,

( $\frac{1}{3}$ × $\frac{4}{7}$ )

LCM of 3 and 7 = 21

( $\frac{7}{21}$ × $\frac{12}{21}$ ) = $\frac{84}{441}$

So,  $\frac{-6}{36}$ +  $\frac{84}{441}$

LCM = 1764

$\frac{-294}{1764}$ + $\frac{336}{1764}$ = $\frac{42}{1764}$

So, 1/42 = 42/1764( after simplifing)

= 1/42 = 1/42

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