Solve ((3/2-1/5)*5-1/10)*3/4-frac{6}{5}=

$$( ( \frac { 3 } { 2 } - \frac { 1 } { 5 } ) \cdot 5 - \frac { 1 } { 10 } ) \cdot \frac { 3 } { 4 } - \frac { 6 } { 5 } =$$

Evaluate

$$\frac{18}{5}=3.6$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{1}{5} to fractions with denominator 10.

$$\left(\left(\frac{15}{10}-\frac{2}{10}\right)\times 5-\frac{1}{10}\right)\times \frac{3}{4}-\frac{6}{5}$$

Since \frac{15}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{15-2}{10}\times 5-\frac{1}{10}\right)\times \frac{3}{4}-\frac{6}{5}$$

Subtract 2 from 15 to get 13.

$$\left(\frac{13}{10}\times 5-\frac{1}{10}\right)\times \frac{3}{4}-\frac{6}{5}$$

Express \frac{13}{10}\times 5 as a single fraction.

$$\left(\frac{13\times 5}{10}-\frac{1}{10}\right)\times \frac{3}{4}-\frac{6}{5}$$

Multiply 13 and 5 to get 65.

$$\left(\frac{65}{10}-\frac{1}{10}\right)\times \frac{3}{4}-\frac{6}{5}$$

Since \frac{65}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-1}{10}\times \frac{3}{4}-\frac{6}{5}$$

Subtract 1 from 65 to get 64.

$$\frac{64}{10}\times \frac{3}{4}-\frac{6}{5}$$

Reduce the fraction \frac{64}{10} to lowest terms by extracting and canceling out 2.

$$\frac{32}{5}\times \frac{3}{4}-\frac{6}{5}$$

Multiply \frac{32}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 3}{5\times 4}-\frac{6}{5}$$

Do the multiplications in the fraction \frac{32\times 3}{5\times 4}.

$$\frac{96}{20}-\frac{6}{5}$$

Reduce the fraction \frac{96}{20} to lowest terms by extracting and canceling out 4.

$$\frac{24}{5}-\frac{6}{5}$$

Since \frac{24}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-6}{5}$$

Subtract 6 from 24 to get 18.

$$\frac{18}{5}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5} = 3\frac{3}{5} = 3.6$$