[514−25×559+(12+34)] is equal to:

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$[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})]$ is equal to:

Options:

A .

\frac{9}{16}

B .

\frac{77}{18}

C .

\frac{24}{12}

D .

\frac{12}{24}

Answer: Option B
:
B

Given $[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})]$
Apply BODMAS rule to solve

= $[\frac{21}{4} - (\frac{2}{5} \times \frac{50}{9}) + \frac{5}{4}]$

= $[\frac{21}{4} - (\frac{20}{9}) + \frac{5}{4}]$

Taking LCM of denominators, we have

$\frac{189 - 80 + 45}{36} = \frac{154}{36} = \frac{77}{18}$
$[5 \frac{1}{4} - \frac{2}{5} \times 5 \frac{5}{9} + (\frac{1}{2} + \frac{3}{4})] = \frac{77}{18}$

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