Solve {[9/2:(7/4-2/5)+3/7*(frac{6}{5}+frac{2}{3})]*frac{3}{5}+frac{13}{25}}*6

$$\{ [ \frac { 9 } { 2 } : ( \frac { 7 } { 4 } - \frac { 2 } { 5 } ) + \frac { 3 } { 7 } \cdot ( \frac { 6 } { 5 } + \frac { 2 } { 3 } ) ] \cdot \frac { 3 } { 5 } + \frac { 13 } { 25 } \} \cdot 6$$

Evaluate

$$18$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{7}{4} and \frac{2}{5} to fractions with denominator 20.

$$\left(\left(\frac{\frac{9}{2}}{\frac{35}{20}-\frac{8}{20}}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Since \frac{35}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\left(\left(\frac{\frac{9}{2}}{\frac{35-8}{20}}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Subtract 8 from 35 to get 27.

$$\left(\left(\frac{\frac{9}{2}}{\frac{27}{20}}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Divide \frac{9}{2} by \frac{27}{20} by multiplying \frac{9}{2} by the reciprocal of \frac{27}{20}.

$$\left(\left(\frac{9}{2}\times \frac{20}{27}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Multiply \frac{9}{2} times \frac{20}{27} by multiplying numerator times numerator and denominator times denominator.

$$\left(\left(\frac{9\times 20}{2\times 27}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Do the multiplications in the fraction \frac{9\times 20}{2\times 27}.

$$\left(\left(\frac{180}{54}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Reduce the fraction \frac{180}{54} to lowest terms by extracting and canceling out 18.

$$\left(\left(\frac{10}{3}+\frac{3}{7}\left(\frac{6}{5}+\frac{2}{3}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{2}{3} to fractions with denominator 15.

$$\left(\left(\frac{10}{3}+\frac{3}{7}\left(\frac{18}{15}+\frac{10}{15}\right)\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Since \frac{18}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\left(\left(\frac{10}{3}+\frac{3}{7}\times \frac{18+10}{15}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Add 18 and 10 to get 28.

$$\left(\left(\frac{10}{3}+\frac{3}{7}\times \frac{28}{15}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Multiply \frac{3}{7} times \frac{28}{15} by multiplying numerator times numerator and denominator times denominator.

$$\left(\left(\frac{10}{3}+\frac{3\times 28}{7\times 15}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Do the multiplications in the fraction \frac{3\times 28}{7\times 15}.

$$\left(\left(\frac{10}{3}+\frac{84}{105}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Reduce the fraction \frac{84}{105} to lowest terms by extracting and canceling out 21.

$$\left(\left(\frac{10}{3}+\frac{4}{5}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Least common multiple of 3 and 5 is 15. Convert \frac{10}{3} and \frac{4}{5} to fractions with denominator 15.

$$\left(\left(\frac{50}{15}+\frac{12}{15}\right)\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Since \frac{50}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\left(\frac{50+12}{15}\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Add 50 and 12 to get 62.

$$\left(\frac{62}{15}\times \frac{3}{5}+\frac{13}{25}\right)\times 6$$

Multiply \frac{62}{15} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{62\times 3}{15\times 5}+\frac{13}{25}\right)\times 6$$

Do the multiplications in the fraction \frac{62\times 3}{15\times 5}.

$$\left(\frac{186}{75}+\frac{13}{25}\right)\times 6$$

Reduce the fraction \frac{186}{75} to lowest terms by extracting and canceling out 3.

$$\left(\frac{62}{25}+\frac{13}{25}\right)\times 6$$

Since \frac{62}{25} and \frac{13}{25} have the same denominator, add them by adding their numerators.

$$\frac{62+13}{25}\times 6$$

Add 62 and 13 to get 75.

$$\frac{75}{25}\times 6$$

Divide 75 by 25 to get 3.

$$3\times 6$$

Multiply 3 and 6 to get 18.

$$18$$

Factor

$$2\times 3^{2}$$