Simplify: \(\left\{\dfrac{12}{27} \div \dfrac{12}{2}\right\} \div \left(\dfrac{1}{11} \times \dfrac{22}{3} + \dfrac{5}{9}\right) + \dfrac{2}{9} \div \dfrac{33}{22} \text{ of } \dfrac{22}{9}\)
\(\dfrac{4}{33}\)
\(\dfrac{12}{27}\div\dfrac{12}{2} = \dfrac{12}{27}\times\dfrac{2}{12} = \dfrac{2}{27}\).
Inside the bracket: \(\dfrac{1}{11}\times\dfrac{22}{3} = \dfrac{2}{3}\), plus \(\dfrac59\) gives \(\dfrac23+\dfrac59 = \dfrac{6+5}{9} = \dfrac{11}{9}\).
First part: \(\dfrac{2}{27}\div\dfrac{11}{9} = \dfrac{2}{27}\times\dfrac{9}{11} = \dfrac{2}{33}\).
For the 'of' term: \(\dfrac{33}{22}\text{ of }\dfrac{22}{9} = \dfrac{33}{22}\times\dfrac{22}{9} = \dfrac{33}{9} = \dfrac{11}{3}\).
Second part: \(\dfrac29\div\dfrac{11}{3} = \dfrac29\times\dfrac{3}{11} = \dfrac{2}{33}\).
Adding both parts: \(\dfrac{2}{33}+\dfrac{2}{33} = \dfrac{4}{33}\).
Hence, the simplified value of the expression is \(\tfrac{4}{33}\).
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Important Questions from Fractions
Which fraction among the following is the least ?
\(\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}\)
Find the value of the following expression:
\(\frac{{3 \div 1 \times 2 + 5 - 2}}{{3 \times 3 - 2}}\)
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
