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Mathematics

Simplify :

(1415÷116+710)×34\Big(\dfrac{14}{15} ÷ 1\dfrac{1}{6} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}

Fractions

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Answer

⇒(1415÷116+710)×34⇒(1415÷76+710)×34⇒(1415×67+710)×34⇒(14×615×7+710)×34⇒(84105+710)×34⇒(45+710)×34⇒(4×25×2+710)×34⇒(810+710)×34⇒(8+710)×34⇒1510×34⇒15×310×4⇒4540⇒98⇒118\Rightarrow \Big(\dfrac{14}{15} ÷ 1\dfrac{1}{6} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{14}{15} ÷ \dfrac{7}{6} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{14}{15} \times \dfrac{6}{7} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{14 \times 6}{15 \times 7} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{84}{105} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{4}{5} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{4 \times 2}{5 \times 2} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{8}{10} + \dfrac{7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \Big(\dfrac{8 + 7}{10}\Big) \times \dfrac{3}{4}\\[1em] \Rightarrow \dfrac{15}{10} \times \dfrac{3}{4}\\[1em] \Rightarrow \dfrac{15 \times 3}{10 \times 4}\\[1em] \Rightarrow \dfrac{45}{40}\\[1em] \Rightarrow \dfrac{9}{8}\\[1em] \Rightarrow 1\dfrac{1}{8}

Hence, (1415÷116+710)×34=118\Big(\dfrac{14}{15} ÷ 1\dfrac{1}{6} + \dfrac{7}{10}\Big) \times \dfrac{3}{4} = 1\dfrac{1}{8}

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