Question 75

What is the value of $$\frac{3}{4} \div \left(\frac{1}{2} + \frac{1}{16}\right) + \frac{2}{3} of \frac{4}{9} \div \left(\frac{1}{3} - \frac{11}{81}\right) + \frac{1}{4} \times \frac{2}{3}$$?

Solution

$$\frac{3}{4} \div \left(\frac{1}{2} + \frac{1}{16}\right) + \frac{2}{3} of \frac{4}{9} \div \left(\frac{1}{3} - \frac{11}{81}\right) + \frac{1}{4} \times \frac{2}{3}$$

$$ \Rightarrow$$ $$\frac{3}{4} \div \frac{9}{16} + \frac{8}{27} \div \frac{16}{81} + \frac{1}{6}$$

$$ \Rightarrow$$ $$\frac{3}{4}\times\frac{16}{9}+\frac{8}{27}\times\frac{81}{16}+\frac{1}{6}$$

$$ \Rightarrow$$ $$\frac{4}{3}+\frac{3}{2}+\frac{1}{6}$$

$$ \Rightarrow$$ 3.


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