Solve 1/6*[(23/10-0.8)div(-1/3)]=

$$\frac { 1 } { 6 } \times [ ( 2 \frac { 3 } { 10 } - 0.8 ) \div ( - \frac { 1 } { 3 } ) ] =$$

Evaluate

$$-0.75$$

Solution Steps

Multiply 2 and 10 to get 20.

$$\frac{1}{6}\times \frac{\frac{20+3}{10}-0.8}{-\frac{1}{3}}$$

Add 20 and 3 to get 23.

$$\frac{1}{6}\times \frac{\frac{23}{10}-0.8}{-\frac{1}{3}}$$

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}\times \frac{\frac{23}{10}-\frac{4}{5}}{-\frac{1}{3}}$$

Least common multiple of 10 and 5 is 10. Convert \frac{23}{10} and \frac{4}{5} to fractions with denominator 10.

$$\frac{1}{6}\times \frac{\frac{23}{10}-\frac{8}{10}}{-\frac{1}{3}}$$

Since \frac{23}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{\frac{23-8}{10}}{-\frac{1}{3}}$$

Subtract 8 from 23 to get 15.

$$\frac{1}{6}\times \frac{\frac{15}{10}}{-\frac{1}{3}}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{6}\times \frac{\frac{3}{2}}{-\frac{1}{3}}$$

Divide \frac{3}{2} by -\frac{1}{3} by multiplying \frac{3}{2} by the reciprocal of -\frac{1}{3}.

$$\frac{1}{6}\times \frac{3}{2}\left(-3\right)$$

Express \frac{3}{2}\left(-3\right) as a single fraction.

$$\frac{1}{6}\times \frac{3\left(-3\right)}{2}$$

Multiply 3 and -3 to get -9.

$$\frac{1}{6}\times \frac{-9}{2}$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$\frac{1}{6}\left(-\frac{9}{2}\right)$$

Multiply \frac{1}{6} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-9\right)}{6\times 2}$$

Do the multiplications in the fraction \frac{1\left(-9\right)}{6\times 2}.

$$\frac{-9}{12}$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{4}$$

Factor

$$-0.75$$