Solve 3/10-5/6+2/3*(-3/8)

$$\frac{ 3 }{ 10 } - \frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } \times (- \frac{ 3 }{ 8 } )$$

Evaluate

$$-\frac{47}{60}\approx -0.783333333$$

Solution Steps

Least common multiple of 10 and 6 is 30. Convert \frac{3}{10} and \frac{5}{6} to fractions with denominator 30.

$$\frac{9}{30}-\frac{25}{30}+\frac{2}{3}\left(-\frac{3}{8}\right)$$

Since \frac{9}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-25}{30}+\frac{2}{3}\left(-\frac{3}{8}\right)$$

Subtract 25 from 9 to get -16.

$$\frac{-16}{30}+\frac{2}{3}\left(-\frac{3}{8}\right)$$

Reduce the fraction \frac{-16}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{8}{15}+\frac{2}{3}\left(-\frac{3}{8}\right)$$

Multiply \frac{2}{3} times -\frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\left(-3\right)}{3\times 8}.

$$-\frac{8}{15}+\frac{-6}{24}$$

Reduce the fraction \frac{-6}{24} to lowest terms by extracting and canceling out 6.

$$-\frac{8}{15}-\frac{1}{4}$$

Least common multiple of 15 and 4 is 60. Convert -\frac{8}{15} and \frac{1}{4} to fractions with denominator 60.

$$-\frac{32}{60}-\frac{15}{60}$$

Since -\frac{32}{60} and \frac{15}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-32-15}{60}$$

Subtract 15 from -32 to get -47.

$$-\frac{47}{60}$$

Factor

$$-\frac{47}{60} = -0.7833333333333333$$