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Addition of Fractions

Simplify : ...

Question

Simplify : $1 + \frac{4}{2 + \frac{3}{5 - \frac{1}{2}}} - \frac{1}{2} (10 \div 2)$ .

A

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B

1

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C

2

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D

3

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Solution

The correct option is A $0$
$1 + \frac{4}{2 + \frac{3}{5 - \frac{1}{2}}} - \frac{1}{2} (10 \div 2) = 1 + \frac{4}{2 + \frac{3}{\frac{10 - 1}{2}}} - \frac{1}{2} \times 5 = 1 + \frac{4}{2 + \frac{3}{\frac{9}{2}}} - \frac{5}{2}$

$= 1 + \frac{4}{2 + 3 \times \frac{2}{9}} - \frac{5}{2} = 1 + \frac{4}{2 + \frac{2}{3}} - \frac{5}{2} = 1 + \frac{4}{\frac{6 + 2}{3}} - \frac{5}{2} = 1 + \frac{4}{\frac{8}{3}} - \frac{5}{2}$

$= 1 + 4 \times \frac{3}{8} - \frac{5}{2} = 1 + \frac{3}{2} - \frac{5}{2} = \frac{5}{2} - \frac{5}{2} = 0$

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