Solve 5/4*[(6/25:3/5+1/2-frac{3}{4})*(frac{11}{4}+frac{14}{3}:8)+frac{3}{5}:2]

$$\frac { 5 } { 4 } \times [ ( \frac { 6 } { 25 } : \frac { 3 } { 5 } + \frac { 1 } { 2 } - \frac { 3 } { 4 } ) \times ( \frac { 11 } { 4 } + \frac { 14 } { 3 } : 8 ) + \frac { 3 } { 5 } : 2 ]$$

Evaluate

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Solution Steps

Divide \frac{6}{25} by \frac{3}{5} by multiplying \frac{6}{25} by the reciprocal of \frac{3}{5}.

$$\frac{5}{4}\left(\left(\frac{6}{25}\times \frac{5}{3}+\frac{1}{2}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Multiply \frac{6}{25} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}\left(\left(\frac{6\times 5}{25\times 3}+\frac{1}{2}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Do the multiplications in the fraction \frac{6\times 5}{25\times 3}.

$$\frac{5}{4}\left(\left(\frac{30}{75}+\frac{1}{2}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Reduce the fraction \frac{30}{75} to lowest terms by extracting and canceling out 15.

$$\frac{5}{4}\left(\left(\frac{2}{5}+\frac{1}{2}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{5}{4}\left(\left(\frac{4}{10}+\frac{5}{10}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Since \frac{4}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}\left(\left(\frac{4+5}{10}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Add 4 and 5 to get 9.

$$\frac{5}{4}\left(\left(\frac{9}{10}-\frac{3}{4}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Least common multiple of 10 and 4 is 20. Convert \frac{9}{10} and \frac{3}{4} to fractions with denominator 20.

$$\frac{5}{4}\left(\left(\frac{18}{20}-\frac{15}{20}\right)\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Since \frac{18}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}\left(\frac{18-15}{20}\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Subtract 15 from 18 to get 3.

$$\frac{5}{4}\left(\frac{3}{20}\left(\frac{11}{4}+\frac{\frac{14}{3}}{8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Express \frac{\frac{14}{3}}{8} as a single fraction.

$$\frac{5}{4}\left(\frac{3}{20}\left(\frac{11}{4}+\frac{14}{3\times 8}\right)+\frac{\frac{3}{5}}{2}\right)$$

Multiply 3 and 8 to get 24.

$$\frac{5}{4}\left(\frac{3}{20}\left(\frac{11}{4}+\frac{14}{24}\right)+\frac{\frac{3}{5}}{2}\right)$$

Reduce the fraction \frac{14}{24} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}\left(\frac{3}{20}\left(\frac{11}{4}+\frac{7}{12}\right)+\frac{\frac{3}{5}}{2}\right)$$

Least common multiple of 4 and 12 is 12. Convert \frac{11}{4} and \frac{7}{12} to fractions with denominator 12.

$$\frac{5}{4}\left(\frac{3}{20}\left(\frac{33}{12}+\frac{7}{12}\right)+\frac{\frac{3}{5}}{2}\right)$$

Since \frac{33}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}\left(\frac{3}{20}\times \frac{33+7}{12}+\frac{\frac{3}{5}}{2}\right)$$

Add 33 and 7 to get 40.

$$\frac{5}{4}\left(\frac{3}{20}\times \frac{40}{12}+\frac{\frac{3}{5}}{2}\right)$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{4}\left(\frac{3}{20}\times \frac{10}{3}+\frac{\frac{3}{5}}{2}\right)$$

Multiply \frac{3}{20} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{4}\left(\frac{3\times 10}{20\times 3}+\frac{\frac{3}{5}}{2}\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{5}{4}\left(\frac{10}{20}+\frac{\frac{3}{5}}{2}\right)$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$\frac{5}{4}\left(\frac{1}{2}+\frac{\frac{3}{5}}{2}\right)$$

Express \frac{\frac{3}{5}}{2} as a single fraction.

$$\frac{5}{4}\left(\frac{1}{2}+\frac{3}{5\times 2}\right)$$

Multiply 5 and 2 to get 10.

$$\frac{5}{4}\left(\frac{1}{2}+\frac{3}{10}\right)$$

Least common multiple of 2 and 10 is 10. Convert \frac{1}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{5}{4}\left(\frac{5}{10}+\frac{3}{10}\right)$$

Since \frac{5}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{5}{4}\times \frac{5+3}{10}$$

Add 5 and 3 to get 8.

$$\frac{5}{4}\times \frac{8}{10}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}\times \frac{4}{5}$$

Cancel out \frac{5}{4} and its reciprocal \frac{4}{5}.

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Factor

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