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Mathematics

Simplify :

323−3113\dfrac{2}{3} - \dfrac{3}{11} of 234÷114×123+132\dfrac{3}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}

Fractions

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Answer

⇒323−311 of 234÷114×123+13⇒323−311×234÷114×123+13⇒323−311×114÷114×123+13⇒323−3×1111×4÷114×123+13⇒323−3×1111×4÷114×123+13⇒323−34÷114×123+13⇒323−34÷54×123+13⇒323−34×45×53+13⇒323−3×4×54×5×3+13⇒323−1+13⇒113+13−1⇒11+13−1⇒123−1⇒4−1⇒3\Rightarrow 3\dfrac{2}{3} - \dfrac{3}{11} \text{ of } 2\dfrac{3}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3}{11} \times 2\dfrac{3}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3}{11} \times \dfrac{11}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3 \times 11}{11 \times 4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3 \times 11}{11 \times 4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3}{4} ÷ \dfrac{5}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3}{4} \times \dfrac{4}{5} \times \dfrac{5}{3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - \dfrac{3 \times 4 \times 5}{4 \times 5 \times 3} + \dfrac{1}{3}\\[1em] \Rightarrow 3\dfrac{2}{3} - 1 + \dfrac{1}{3}\\[1em] \Rightarrow \dfrac{11}{3} + \dfrac{1}{3} - 1\\[1em] \Rightarrow \dfrac{11 + 1}{3} - 1\\[1em] \Rightarrow \dfrac{12}{3} - 1\\[1em] \Rightarrow 4 - 1\\[1em] \Rightarrow 3

Hence, 323−3113\dfrac{2}{3} - \dfrac{3}{11} of 234÷114×123+13=32\dfrac{3}{4} ÷ 1\dfrac{1}{4} \times 1\dfrac{2}{3} + \dfrac{1}{3} = 3.

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