Solve (3/2-4/5)*2-3/5:frac{3/4}{frac{1}{10}+1}=

$$\frac { ( \frac { 3 } { 2 } - \frac { 4 } { 5 } ) \cdot 2 - \frac { 3 } { 5 } : \frac { 3 } { 4 } } { \frac { 1 } { 10 } + 1 } =$$

Evaluate

$$\frac{6}{11}\approx 0.545454545$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\left(\frac{15}{10}-\frac{8}{10}\right)\times 2-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

Since \frac{15}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-8}{10}\times 2-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{7}{10}\times 2-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

Express \frac{7}{10}\times 2 as a single fraction.

$$\frac{\frac{7\times 2}{10}-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{14}{10}-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{5}-\frac{\frac{3}{5}}{\frac{3}{4}}}{\frac{1}{10}+1}$$

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

$$\frac{\frac{7}{5}-\frac{3}{5}\times \frac{4}{3}}{\frac{1}{10}+1}$$

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

$$\frac{\frac{7}{5}-\frac{3\times 4}{5\times 3}}{\frac{1}{10}+1}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{7}{5}-\frac{4}{5}}{\frac{1}{10}+1}$$

Since \frac{7}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-4}{5}}{\frac{1}{10}+1}$$

Subtract 4 from 7 to get 3.

$$\frac{\frac{3}{5}}{\frac{1}{10}+1}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{3}{5}}{\frac{1}{10}+\frac{10}{10}}$$

Since \frac{1}{10} and \frac{10}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}}{\frac{1+10}{10}}$$

Add 1 and 10 to get 11.

$$\frac{\frac{3}{5}}{\frac{11}{10}}$$

Divide \frac{3}{5} by \frac{11}{10} by multiplying \frac{3}{5} by the reciprocal of \frac{11}{10}.

$$\frac{3}{5}\times \frac{10}{11}$$

Multiply \frac{3}{5} times \frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{5\times 11}$$

Do the multiplications in the fraction \frac{3\times 10}{5\times 11}.

$$\frac{30}{55}$$

Reduce the fraction \frac{30}{55} to lowest terms by extracting and canceling out 5.

$$\frac{6}{11}$$

Factor

$$\frac{2 \cdot 3}{11} = 0.5454545454545454$$