Solve 1/2*(-5/6)-(-10/6)+(1/2divfrac{15}{6})=

$$\frac { 1 } { 2 } \times ( \frac { - 5 } { 6 } ) - ( \frac { - 10 } { 6 } ) + ( \frac { 1 } { 2 } \div \frac { 15 } { 6 } ) =$$

Evaluate

$$\frac{29}{20}=1.45$$

Solution Steps

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{1}{2}\left(-\frac{5}{6}\right)-\frac{-10}{6}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Multiply \frac{1}{2} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-5\right)}{2\times 6}-\frac{-10}{6}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 6}.

$$\frac{-5}{12}-\frac{-10}{6}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$-\frac{5}{12}-\frac{-10}{6}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

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

$$-\frac{5}{12}-\left(-\frac{5}{3}\right)+\frac{\frac{1}{2}}{\frac{15}{6}}$$

The opposite of -\frac{5}{3} is \frac{5}{3}.

$$-\frac{5}{12}+\frac{5}{3}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

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

$$-\frac{5}{12}+\frac{20}{12}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Since -\frac{5}{12} and \frac{20}{12} have the same denominator, add them by adding their numerators.

$$\frac{-5+20}{12}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Add -5 and 20 to get 15.

$$\frac{15}{12}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Reduce the fraction \frac{15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{5}{4}+\frac{\frac{1}{2}}{\frac{15}{6}}$$

Divide \frac{1}{2} by \frac{15}{6} by multiplying \frac{1}{2} by the reciprocal of \frac{15}{6}.

$$\frac{5}{4}+\frac{6}{2\times 15}$$

Multiply 2 and 15 to get 30.

$$\frac{5}{4}+\frac{6}{30}$$

Reduce the fraction \frac{6}{30} to lowest terms by extracting and canceling out 6.

$$\frac{5}{4}+\frac{1}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{5}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{25}{20}+\frac{4}{20}$$

Since \frac{25}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{25+4}{20}$$

Add 25 and 4 to get 29.

$$\frac{29}{20}$$

Factor

$$\frac{29}{2 ^ {2} \cdot 5} = 1\frac{9}{20} = 1.45$$