Question:- [tex]( \frac{ - 3}{4} .. \frac{2}{3} .. \frac{ - 5}{6} )rationa \: nmbers \: distunutive \\ \: of \: multipivatiom[/tex] ​

Answer:-

[tex]To \: understand \: this, \: consider \: the \: rational \\ numbers( \frac{ - 3}{4}.. \frac{2}{3}.. \frac{ - 5}{6} ) [/tex]

[tex] \frac{ - 3}{4} \times( \frac{2}{3} + ( \frac{ - 5}{6} ) = \frac{ - 3}{4} \times ( \frac{(4) + ( - 5)}{6} )[/tex]

[tex] = \frac{ - 3}{4} \times ( \frac{ - 1}{6} ) = \frac{3}{24} = \frac{1}{8} [/tex]

[tex] \frac{ - 3}{4} \times \frac{2}{3} = \frac{ - 3 \times 2}{4 \times 3} = \frac{ - 6}{12} = \frac{ - 1}{2} [/tex]

[tex]and \: \frac{ - 3}{4} \times \frac{ - 5}{6} = \frac{5}{8} [/tex]

[tex]therefore \: ( \frac{ - 3}{4} \times \frac{2}{3} ) + ( \frac{ - 3}{4} \times \frac{ - 5}{6} ) = \frac{ - 1}{2} + \frac{5}{8} = \frac{1}{8} [/tex]

[tex]thus.. \frac{ - 3}{4} \times ( \frac{2}{3} + \frac{ - 5}{6} ) = ( \frac{ - 3}{4} \times \frac{2}{3} ) + ( \frac{ - 3}{4} \times \frac{ - 5}{6} )[/tex]

[tex]distributivity \: of \: multiplication \: over \: \\addition \: for \: rational \: numbers[/tex]

Answer:-

[tex]= \frac{ - 3}{4} \times ( \frac{ - 1}{6} )= \frac{3}{24} = \frac{1}{8}=[/tex]

[tex]\frac{ - 3}{4} \times \frac{2}{3} = \frac{ - 3 \times 2}{4 \times 3} = \frac{ - 6}{12} = \frac{ - 1}{2}[/tex]

[tex]\frac{ - 3}{4} \times \frac{ - 5}{6} = \frac{5}{8}[/tex]

[tex]\frac{ - 3}{4} \times \frac{2}{3} ) + ( \frac{ - 3}{4} \times \frac{ - 5}{6} ) = \frac{ - 1}{2} + \frac{5}{8} = \frac{1}{8}[/tex]

[tex] \frac{ - 3}{4} \times ( \frac{2}{3} + \frac{ - 5}{6} ) = ( \frac{ - 3}{4} \times \frac{2}{3} ) + ( \frac{ - 3}{4} \times \frac{ - 5}{6} )[/tex]

Property used here distributive