Question

using appropriate property solve 3/5×2/7+1/7×3/4-2/7×-9/11 step by step​

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{3}{5}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}-\dfrac{2}{7}{\times}\left(\dfrac{-9}{11}\right)}$

$\textbf{To simplify:}$

$\mathsf{\dfrac{3}{5}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}-\dfrac{2}{7}{\times}\left(\dfrac{-9}{11}\right)}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{3}{5}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}-\dfrac{2}{7}{\times}\left(\dfrac{-9}{11}\right)}$

$\mathsf{=\dfrac{3}{5}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}+\dfrac{2}{7}{\times}\dfrac{9}{11}}$

$\mathsf{=\left(\dfrac{3}{5}{\times}\dfrac{2}{7}+\dfrac{9}{11}{\times}\dfrac{2}{7}\right)+\dfrac{1}{7}{\times}\dfrac{3}{4}}$

$\mathsf{Using,}$

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

$\mathsf{=\left(\dfrac{3}{5}+\dfrac{9}{11}\right){\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}}$

$\mathsf{=\dfrac{33+45}{55}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}}$

$\mathsf{=\dfrac{78}{55}{\times}\dfrac{2}{7}+\dfrac{1}{7}{\times}\dfrac{3}{4}}$

$\mathsf{=\dfrac{156}{55}{\times}\dfrac{1}{7}+\dfrac{3}{4}{\times}\dfrac{1}{7}}$

$\mathsf{=\left(\dfrac{156}{55}+\dfrac{3}{4}\right){\times}\dfrac{1}{7}}$

$\mathsf{=\left(\dfrac{156}{55}+\dfrac{3}{4}\right){\times}\dfrac{1}{7}}$

$\mathsf{=\dfrac{624+165}{220}{\times}\dfrac{1}{7}}$

$\mathsf{=\dfrac{789}{220}{\times}\dfrac{1}{7}}$

$\mathsf{=\dfrac{789}{1540}}$

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