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 \(\tfrac{4}{33}\).
Similar Questions
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can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
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What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
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Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
