Solve 5/3div[(7/8-3/4)*8/5+frac{2}{5}]*3*3

$$\frac { 5 } { 3 } \div [ ( \frac { 7 } { 8 } - \frac { 3 } { 4 } ) \times \frac { 8 } { 5 } + \frac { 2 } { 5 } ] \times 3 \times 3$$

Evaluate

$$25$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{7}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{\frac{5}{3}}{\left(\frac{7}{8}-\frac{6}{8}\right)\times \frac{8}{5}+\frac{2}{5}}\times 3\times 3$$

Since \frac{7}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{3}}{\frac{7-6}{8}\times \frac{8}{5}+\frac{2}{5}}\times 3\times 3$$

Subtract 6 from 7 to get 1.

$$\frac{\frac{5}{3}}{\frac{1}{8}\times \frac{8}{5}+\frac{2}{5}}\times 3\times 3$$

Multiply \frac{1}{8} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{3}}{\frac{1\times 8}{8\times 5}+\frac{2}{5}}\times 3\times 3$$

Cancel out 8 in both numerator and denominator.

$$\frac{\frac{5}{3}}{\frac{1}{5}+\frac{2}{5}}\times 3\times 3$$

Since \frac{1}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{3}}{\frac{1+2}{5}}\times 3\times 3$$

Add 1 and 2 to get 3.

$$\frac{\frac{5}{3}}{\frac{3}{5}}\times 3\times 3$$

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

$$\frac{5}{3}\times \frac{5}{3}\times 3\times 3$$

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

$$\frac{5\times 5}{3\times 3}\times 3\times 3$$

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

$$\frac{25}{9}\times 3\times 3$$

Express \frac{25}{9}\times 3 as a single fraction.

$$\frac{25\times 3}{9}\times 3$$

Multiply 25 and 3 to get 75.

$$\frac{75}{9}\times 3$$

Reduce the fraction \frac{75}{9} to lowest terms by extracting and canceling out 3.

$$\frac{25}{3}\times 3$$

Cancel out 3 and 3.

$$25$$

Factor

$$5^{2}$$