Solve (-1)^3/15+(-2/3)^2:22/3-|-5/6|

$$\frac { ( - 1 ) ^ { 3 } } { 15 } + ( - \frac { 2 } { 3 } ) ^ { 2 } : 2 \frac { 2 } { 3 } - | - \frac { 5 } { 6 } |$$

Evaluate

$$-\frac{11}{15}\approx -0.733333333$$

Solution Steps

Calculate -1 to the power of 3 and get -1.

$$\frac{-1}{15}+\frac{\left(-\frac{2}{3}\right)^{2}}{\frac{2\times 3+2}{3}}-|-\frac{5}{6}|$$

Fraction \frac{-1}{15} can be rewritten as -\frac{1}{15} by extracting the negative sign.

$$-\frac{1}{15}+\frac{\left(-\frac{2}{3}\right)^{2}}{\frac{2\times 3+2}{3}}-|-\frac{5}{6}|$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$-\frac{1}{15}+\frac{\frac{4}{9}}{\frac{2\times 3+2}{3}}-|-\frac{5}{6}|$$

Multiply 2 and 3 to get 6.

$$-\frac{1}{15}+\frac{\frac{4}{9}}{\frac{6+2}{3}}-|-\frac{5}{6}|$$

Add 6 and 2 to get 8.

$$-\frac{1}{15}+\frac{\frac{4}{9}}{\frac{8}{3}}-|-\frac{5}{6}|$$

Divide \frac{4}{9} by \frac{8}{3} by multiplying \frac{4}{9} by the reciprocal of \frac{8}{3}.

$$-\frac{1}{15}+\frac{4}{9}\times \frac{3}{8}-|-\frac{5}{6}|$$

Multiply \frac{4}{9} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{15}+\frac{4\times 3}{9\times 8}-|-\frac{5}{6}|$$

Do the multiplications in the fraction \frac{4\times 3}{9\times 8}.

$$-\frac{1}{15}+\frac{12}{72}-|-\frac{5}{6}|$$

Reduce the fraction \frac{12}{72} to lowest terms by extracting and canceling out 12.

$$-\frac{1}{15}+\frac{1}{6}-|-\frac{5}{6}|$$

Least common multiple of 15 and 6 is 30. Convert -\frac{1}{15} and \frac{1}{6} to fractions with denominator 30.

$$-\frac{2}{30}+\frac{5}{30}-|-\frac{5}{6}|$$

Since -\frac{2}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{-2+5}{30}-|-\frac{5}{6}|$$

Add -2 and 5 to get 3.

$$\frac{3}{30}-|-\frac{5}{6}|$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}-|-\frac{5}{6}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{6} is \frac{5}{6}.

$$\frac{1}{10}-\frac{5}{6}$$

Least common multiple of 10 and 6 is 30. Convert \frac{1}{10} and \frac{5}{6} to fractions with denominator 30.

$$\frac{3}{30}-\frac{25}{30}$$

Since \frac{3}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-25}{30}$$

Subtract 25 from 3 to get -22.

$$\frac{-22}{30}$$

Reduce the fraction \frac{-22}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{15}$$

Factor

$$-\frac{11}{15} = -0.7333333333333333$$