Solve 1-{3/4+3*4div(-2)^3+2}div5/6

$$1 - \{ \frac { 3 } { 4 } + 3 \times 4 \div ( - 2 ) ^ { 3 } + 2 \} \div \frac { 5 } { 6 }$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Multiply 3 and 4 to get 12.

$$1-\frac{\frac{3}{4}+\frac{12}{\left(-2\right)^{3}}+2}{\frac{5}{6}}$$

Calculate -2 to the power of 3 and get -8.

$$1-\frac{\frac{3}{4}+\frac{12}{-8}+2}{\frac{5}{6}}$$

Reduce the fraction \frac{12}{-8} to lowest terms by extracting and canceling out 4.

$$1-\frac{\frac{3}{4}-\frac{3}{2}+2}{\frac{5}{6}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{3}{2} to fractions with denominator 4.

$$1-\frac{\frac{3}{4}-\frac{6}{4}+2}{\frac{5}{6}}$$

Since \frac{3}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{\frac{3-6}{4}+2}{\frac{5}{6}}$$

Subtract 6 from 3 to get -3.

$$1-\frac{-\frac{3}{4}+2}{\frac{5}{6}}$$

Convert 2 to fraction \frac{8}{4}.

$$1-\frac{-\frac{3}{4}+\frac{8}{4}}{\frac{5}{6}}$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$1-\frac{\frac{-3+8}{4}}{\frac{5}{6}}$$

Add -3 and 8 to get 5.

$$1-\frac{\frac{5}{4}}{\frac{5}{6}}$$

Divide \frac{5}{4} by \frac{5}{6} by multiplying \frac{5}{4} by the reciprocal of \frac{5}{6}.

$$1-\frac{5}{4}\times \frac{6}{5}$$

Multiply \frac{5}{4} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{5\times 6}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$1-\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

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

$$\frac{2}{2}-\frac{3}{2}$$

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

$$\frac{2-3}{2}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$