Solve 2-1/20/frac{3{4}-4/5}+6/5=

$$\frac { 2 - \frac { 1 } { 20 } } { \frac { 3 } { 4 } - \frac { 4 } { 5 } } + \frac { 6 } { 5 } =$$

Evaluate

$$-\frac{189}{5}=-37.8$$

Solution Steps

Convert 2 to fraction \frac{40}{20}.

$$\frac{\frac{40}{20}-\frac{1}{20}}{\frac{3}{4}-\frac{4}{5}}+\frac{6}{5}$$

Since \frac{40}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-1}{20}}{\frac{3}{4}-\frac{4}{5}}+\frac{6}{5}$$

Subtract 1 from 40 to get 39.

$$\frac{\frac{39}{20}}{\frac{3}{4}-\frac{4}{5}}+\frac{6}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{\frac{39}{20}}{\frac{15}{20}-\frac{16}{20}}+\frac{6}{5}$$

Since \frac{15}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{39}{20}}{\frac{15-16}{20}}+\frac{6}{5}$$

Subtract 16 from 15 to get -1.

$$\frac{\frac{39}{20}}{-\frac{1}{20}}+\frac{6}{5}$$

Divide \frac{39}{20} by -\frac{1}{20} by multiplying \frac{39}{20} by the reciprocal of -\frac{1}{20}.

$$\frac{39}{20}\left(-20\right)+\frac{6}{5}$$

Express \frac{39}{20}\left(-20\right) as a single fraction.

$$\frac{39\left(-20\right)}{20}+\frac{6}{5}$$

Multiply 39 and -20 to get -780.

$$\frac{-780}{20}+\frac{6}{5}$$

Divide -780 by 20 to get -39.

$$-39+\frac{6}{5}$$

Convert -39 to fraction -\frac{195}{5}.

$$-\frac{195}{5}+\frac{6}{5}$$

Since -\frac{195}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$\frac{-195+6}{5}$$

Add -195 and 6 to get -189.

$$-\frac{189}{5}$$

Factor

$$-\frac{189}{5} = -37\frac{4}{5} = -37.8$$