Solve -4/25+7/20/frac{6{40}-1/5}

$$\frac { \frac { - 4 } { 25 } + \frac { 7 } { 20 } } { \frac { 6 } { 40 } - \frac { 1 } { 5 } }$$

Evaluate

$$-\frac{19}{5}=-3.8$$

Solution Steps

Fraction \frac{-4}{25} can be rewritten as -\frac{4}{25} by extracting the negative sign.

$$\frac{-\frac{4}{25}+\frac{7}{20}}{\frac{6}{40}-\frac{1}{5}}$$

Least common multiple of 25 and 20 is 100. Convert -\frac{4}{25} and \frac{7}{20} to fractions with denominator 100.

$$\frac{-\frac{16}{100}+\frac{35}{100}}{\frac{6}{40}-\frac{1}{5}}$$

Since -\frac{16}{100} and \frac{35}{100} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-16+35}{100}}{\frac{6}{40}-\frac{1}{5}}$$

Add -16 and 35 to get 19.

$$\frac{\frac{19}{100}}{\frac{6}{40}-\frac{1}{5}}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{19}{100}}{\frac{3}{20}-\frac{1}{5}}$$

Least common multiple of 20 and 5 is 20. Convert \frac{3}{20} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{19}{100}}{\frac{3}{20}-\frac{4}{20}}$$

Since \frac{3}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{100}}{\frac{3-4}{20}}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{19}{100}}{-\frac{1}{20}}$$

Divide \frac{19}{100} by -\frac{1}{20} by multiplying \frac{19}{100} by the reciprocal of -\frac{1}{20}.

$$\frac{19}{100}\left(-20\right)$$

Express \frac{19}{100}\left(-20\right) as a single fraction.

$$\frac{19\left(-20\right)}{100}$$

Multiply 19 and -20 to get -380.

$$\frac{-380}{100}$$

Reduce the fraction \frac{-380}{100} to lowest terms by extracting and canceling out 20.

$$-\frac{19}{5}$$

Factor

$$-\frac{19}{5} = -3\frac{4}{5} = -3.8$$