Solve 18/99*11/10/(frac{3{2}+25/10)^2}+frac{1}{10}

$$\frac { \frac { 18 } { 99 } \cdot \frac { 11 } { 10 } } { ( \frac { 3 } { 2 } + \frac { 25 } { 10 } ) ^ { 2 } } + \frac { 1 } { 10 }$$

Evaluate

$$\frac{9}{80}=0.1125$$

Solution Steps

Reduce the fraction \frac{18}{99} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{2}{11}\times \frac{11}{10}}{\left(\frac{3}{2}+\frac{25}{10}\right)^{2}}+\frac{1}{10}$$

Multiply \frac{2}{11} and \frac{11}{10} to get \frac{1}{5}.

$$\frac{\frac{1}{5}}{\left(\frac{3}{2}+\frac{25}{10}\right)^{2}}+\frac{1}{10}$$

Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{1}{5}}{\left(\frac{3}{2}+\frac{5}{2}\right)^{2}}+\frac{1}{10}$$

Add \frac{3}{2} and \frac{5}{2} to get 4.

$$\frac{\frac{1}{5}}{4^{2}}+\frac{1}{10}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\frac{1}{5}}{16}+\frac{1}{10}$$

Express \frac{\frac{1}{5}}{16} as a single fraction.

$$\frac{1}{5\times 16}+\frac{1}{10}$$

Multiply 5 and 16 to get 80.

$$\frac{1}{80}+\frac{1}{10}$$

Add \frac{1}{80} and \frac{1}{10} to get \frac{9}{80}.

$$\frac{9}{80}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4} \cdot 5} = 0.1125$$