Solve 3/5*3/4div2/3/frac{3{5}}+1

$$\frac { \frac { 3 } { 5 } \times \frac { 3 } { 4 } \div \frac { 2 } { 3 } } { \frac { 3 } { 5 } } + 1$$

Evaluate

$$\frac{17}{8}=2.125$$

Solution Steps

Divide \frac{\frac{3}{5}\times \frac{3}{4}}{\frac{2}{3}} by \frac{3}{5} by multiplying \frac{\frac{3}{5}\times \frac{3}{4}}{\frac{2}{3}} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{3}{5}\times \frac{3}{4}\times 5}{\frac{2}{3}\times 3}+1$$

Multiply \frac{3}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 3}{5\times 4}\times 5}{\frac{2}{3}\times 3}+1$$

Do the multiplications in the fraction \frac{3\times 3}{5\times 4}.

$$\frac{\frac{9}{20}\times 5}{\frac{2}{3}\times 3}+1$$

Express \frac{9}{20}\times 5 as a single fraction.

$$\frac{\frac{9\times 5}{20}}{\frac{2}{3}\times 3}+1$$

Multiply 9 and 5 to get 45.

$$\frac{\frac{45}{20}}{\frac{2}{3}\times 3}+1$$

Reduce the fraction \frac{45}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{4}}{\frac{2}{3}\times 3}+1$$

Cancel out 3 and 3.

$$\frac{\frac{9}{4}}{2}+1$$

Express \frac{\frac{9}{4}}{2} as a single fraction.

$$\frac{9}{4\times 2}+1$$

Multiply 4 and 2 to get 8.

$$\frac{9}{8}+1$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{9}{8}+\frac{8}{8}$$

Since \frac{9}{8} and \frac{8}{8} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{8}$$

Add 9 and 8 to get 17.

$$\frac{17}{8}$$

Factor

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2.125$$