Solve -5/6:(-3+7/2)-1/2*[-3*(1/2-frac{1}{1})+1]

$$- \frac { 5 } { 6 } : ( - 3 + \frac { 7 } { 2 } ) - \frac { 1 } { 2 } \cdot [ - 3 \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 1 } ) + 1 ]$$

Evaluate

$$-\frac{35}{12}\approx -2.916666667$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{-\frac{5}{6}}{-3+\frac{7}{2}}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Convert -3 to fraction -\frac{6}{2}.

$$\frac{-\frac{5}{6}}{-\frac{6}{2}+\frac{7}{2}}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Since -\frac{6}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{6}}{\frac{-6+7}{2}}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Add -6 and 7 to get 1.

$$\frac{-\frac{5}{6}}{\frac{1}{2}}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Divide -\frac{5}{6} by \frac{1}{2} by multiplying -\frac{5}{6} by the reciprocal of \frac{1}{2}.

$$-\frac{5}{6}\times 2-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Express -\frac{5}{6}\times 2 as a single fraction.

$$\frac{-5\times 2}{6}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Multiply -5 and 2 to get -10.

$$\frac{-10}{6}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{3}-\frac{1}{2}\left(-3\left(\frac{1}{2}-1\right)+1\right)$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{3}-\frac{1}{2}\left(-3\left(\frac{1}{2}-\frac{2}{2}\right)+1\right)$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{3}-\frac{1}{2}\left(-3\times \frac{1-2}{2}+1\right)$$

Subtract 2 from 1 to get -1.

$$-\frac{5}{3}-\frac{1}{2}\left(-3\left(-\frac{1}{2}\right)+1\right)$$

Express -3\left(-\frac{1}{2}\right) as a single fraction.

$$-\frac{5}{3}-\frac{1}{2}\left(\frac{-3\left(-1\right)}{2}+1\right)$$

Multiply -3 and -1 to get 3.

$$-\frac{5}{3}-\frac{1}{2}\left(\frac{3}{2}+1\right)$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{3}-\frac{1}{2}\left(\frac{3}{2}+\frac{2}{2}\right)$$

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$-\frac{5}{3}-\frac{1}{2}\times \frac{3+2}{2}$$

Add 3 and 2 to get 5.

$$-\frac{5}{3}-\frac{1}{2}\times \frac{5}{2}$$

Multiply \frac{1}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{3}-\frac{1\times 5}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 2}.

$$-\frac{5}{3}-\frac{5}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{5}{3} and \frac{5}{4} to fractions with denominator 12.

$$-\frac{20}{12}-\frac{15}{12}$$

Since -\frac{20}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-15}{12}$$

Subtract 15 from -20 to get -35.

$$-\frac{35}{12}$$

Factor

$$-\frac{35}{12} = -2\frac{11}{12} \approx -2.916666667$$