Solve (244/9*23/11)*[5/4:(4+22/7)+frac{37}{20}]

$$( 24 \frac { 4 } { 9 } \cdot \frac { 23 } { 11 } ) \cdot [ \frac { 5 } { 4 } : ( 4 + \frac { 22 } { 7 } ) + \frac { 37 } { 20 } ]$$

Evaluate

$$\frac{207}{2}=103.5$$

Solution Steps

Multiply 24 and 9 to get 216.

$$\frac{216+4}{9}\times \frac{23}{11}\left(\frac{\frac{5}{4}}{4+\frac{22}{7}}+\frac{37}{20}\right)$$

Add 216 and 4 to get 220.

$$\frac{220}{9}\times \frac{23}{11}\left(\frac{\frac{5}{4}}{4+\frac{22}{7}}+\frac{37}{20}\right)$$

Multiply \frac{220}{9} times \frac{23}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{220\times 23}{9\times 11}\left(\frac{\frac{5}{4}}{4+\frac{22}{7}}+\frac{37}{20}\right)$$

Do the multiplications in the fraction \frac{220\times 23}{9\times 11}.

$$\frac{5060}{99}\left(\frac{\frac{5}{4}}{4+\frac{22}{7}}+\frac{37}{20}\right)$$

Reduce the fraction \frac{5060}{99} to lowest terms by extracting and canceling out 11.

$$\frac{460}{9}\left(\frac{\frac{5}{4}}{4+\frac{22}{7}}+\frac{37}{20}\right)$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{460}{9}\left(\frac{\frac{5}{4}}{\frac{28}{7}+\frac{22}{7}}+\frac{37}{20}\right)$$

Since \frac{28}{7} and \frac{22}{7} have the same denominator, add them by adding their numerators.

$$\frac{460}{9}\left(\frac{\frac{5}{4}}{\frac{28+22}{7}}+\frac{37}{20}\right)$$

Add 28 and 22 to get 50.

$$\frac{460}{9}\left(\frac{\frac{5}{4}}{\frac{50}{7}}+\frac{37}{20}\right)$$

Divide \frac{5}{4} by \frac{50}{7} by multiplying \frac{5}{4} by the reciprocal of \frac{50}{7}.

$$\frac{460}{9}\left(\frac{5}{4}\times \frac{7}{50}+\frac{37}{20}\right)$$

Multiply \frac{5}{4} times \frac{7}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{460}{9}\left(\frac{5\times 7}{4\times 50}+\frac{37}{20}\right)$$

Do the multiplications in the fraction \frac{5\times 7}{4\times 50}.

$$\frac{460}{9}\left(\frac{35}{200}+\frac{37}{20}\right)$$

Reduce the fraction \frac{35}{200} to lowest terms by extracting and canceling out 5.

$$\frac{460}{9}\left(\frac{7}{40}+\frac{37}{20}\right)$$

Least common multiple of 40 and 20 is 40. Convert \frac{7}{40} and \frac{37}{20} to fractions with denominator 40.

$$\frac{460}{9}\left(\frac{7}{40}+\frac{74}{40}\right)$$

Since \frac{7}{40} and \frac{74}{40} have the same denominator, add them by adding their numerators.

$$\frac{460}{9}\times \frac{7+74}{40}$$

Add 7 and 74 to get 81.

$$\frac{460}{9}\times \frac{81}{40}$$

Multiply \frac{460}{9} times \frac{81}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{460\times 81}{9\times 40}$$

Do the multiplications in the fraction \frac{460\times 81}{9\times 40}.

$$\frac{37260}{360}$$

Reduce the fraction \frac{37260}{360} to lowest terms by extracting and canceling out 180.

$$\frac{207}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 23}{2} = 103\frac{1}{2} = 103.5$$