Solve -4/25+7/20div-6/40-1/5=

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

Evaluate

$$-\frac{202}{75}\approx -2.693333333$$

Solution Steps

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

$$-\frac{4}{25}+\frac{\frac{7}{20}}{-\frac{3}{20}}-\frac{1}{5}$$

Divide \frac{7}{20} by -\frac{3}{20} by multiplying \frac{7}{20} by the reciprocal of -\frac{3}{20}.

$$-\frac{4}{25}+\frac{7}{20}\left(-\frac{20}{3}\right)-\frac{1}{5}$$

Multiply \frac{7}{20} times -\frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{25}+\frac{7\left(-20\right)}{20\times 3}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{7\left(-20\right)}{20\times 3}.

$$-\frac{4}{25}+\frac{-140}{60}-\frac{1}{5}$$

Reduce the fraction \frac{-140}{60} to lowest terms by extracting and canceling out 20.

$$-\frac{4}{25}-\frac{7}{3}-\frac{1}{5}$$

Least common multiple of 25 and 3 is 75. Convert -\frac{4}{25} and \frac{7}{3} to fractions with denominator 75.

$$-\frac{12}{75}-\frac{175}{75}-\frac{1}{5}$$

Since -\frac{12}{75} and \frac{175}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-12-175}{75}-\frac{1}{5}$$

Subtract 175 from -12 to get -187.

$$-\frac{187}{75}-\frac{1}{5}$$

Least common multiple of 75 and 5 is 75. Convert -\frac{187}{75} and \frac{1}{5} to fractions with denominator 75.

$$-\frac{187}{75}-\frac{15}{75}$$

Since -\frac{187}{75} and \frac{15}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-187-15}{75}$$

Subtract 15 from -187 to get -202.

$$-\frac{202}{75}$$

Factor

$$-\frac{202}{75} = -2\frac{52}{75} = -2.6933333333333334$$