Solve 22/7(frac{18/2frac{2{7}+2})(18/2frac{2{1}}+2)}{2}

$$\frac { \frac { 22 } { 7 } ( \frac { 18 } { 2 \frac { 2 } { 7 } + 2 } ) ( \frac { 18 } { 2 \frac { 2 } { 1 } } + 2 ) } { 2 }$$

Evaluate

$$\frac{429}{10}=42.9$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{22}{7}\times \frac{18}{\frac{14+2}{7}+2}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Add 14 and 2 to get 16.

$$\frac{\frac{22}{7}\times \frac{18}{\frac{16}{7}+2}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{\frac{22}{7}\times \frac{18}{\frac{16}{7}+\frac{14}{7}}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Since \frac{16}{7} and \frac{14}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22}{7}\times \frac{18}{\frac{16+14}{7}}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Add 16 and 14 to get 30.

$$\frac{\frac{22}{7}\times \frac{18}{\frac{30}{7}}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Divide 18 by \frac{30}{7} by multiplying 18 by the reciprocal of \frac{30}{7}.

$$\frac{\frac{22}{7}\times 18\times \frac{7}{30}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Express 18\times \frac{7}{30} as a single fraction.

$$\frac{\frac{22}{7}\times \frac{18\times 7}{30}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Multiply 18 and 7 to get 126.

$$\frac{\frac{22}{7}\times \frac{126}{30}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Reduce the fraction \frac{126}{30} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{22}{7}\times \frac{21}{5}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Multiply \frac{22}{7} times \frac{21}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{22\times 21}{7\times 5}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Do the multiplications in the fraction \frac{22\times 21}{7\times 5}.

$$\frac{\frac{462}{35}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Reduce the fraction \frac{462}{35} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{66}{5}\left(\frac{18}{\frac{2\times 1+2}{1}}+2\right)}{2}$$

Divide 18 by \frac{2\times 1+2}{1} by multiplying 18 by the reciprocal of \frac{2\times 1+2}{1}.

$$\frac{\frac{66}{5}\left(\frac{18}{2\times 1+2}+2\right)}{2}$$

Multiply 2 and 1 to get 2.

$$\frac{\frac{66}{5}\left(\frac{18}{2+2}+2\right)}{2}$$

Add 2 and 2 to get 4.

$$\frac{\frac{66}{5}\left(\frac{18}{4}+2\right)}{2}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{66}{5}\left(\frac{9}{2}+2\right)}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{66}{5}\left(\frac{9}{2}+\frac{4}{2}\right)}{2}$$

Since \frac{9}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{66}{5}\times \frac{9+4}{2}}{2}$$

Add 9 and 4 to get 13.

$$\frac{\frac{66}{5}\times \frac{13}{2}}{2}$$

Multiply \frac{66}{5} times \frac{13}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{66\times 13}{5\times 2}}{2}$$

Do the multiplications in the fraction \frac{66\times 13}{5\times 2}.

$$\frac{\frac{858}{10}}{2}$$

Reduce the fraction \frac{858}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{429}{5}}{2}$$

Express \frac{\frac{429}{5}}{2} as a single fraction.

$$\frac{429}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{429}{10}$$

Factor

$$\frac{3 \cdot 11 \cdot 13}{2 \cdot 5} = 42\frac{9}{10} = 42.9$$