Solve 1/3+2(2-1/2)div(-4/5)+1

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

Evaluate

$$-\frac{29}{12}\approx -2.416666667$$

Solution Steps

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

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 4 to get 3.

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

Cancel out 2 and 2.

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

Divide 3 by -\frac{4}{5} by multiplying 3 by the reciprocal of -\frac{4}{5}.

$$\frac{1}{3}+3\left(-\frac{5}{4}\right)+1$$

Express 3\left(-\frac{5}{4}\right) as a single fraction.

$$\frac{1}{3}+\frac{3\left(-5\right)}{4}+1$$

Multiply 3 and -5 to get -15.

$$\frac{1}{3}+\frac{-15}{4}+1$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{1}{3}-\frac{15}{4}+1$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{15}{4} to fractions with denominator 12.

$$\frac{4}{12}-\frac{45}{12}+1$$

Since \frac{4}{12} and \frac{45}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-45}{12}+1$$

Subtract 45 from 4 to get -41.

$$-\frac{41}{12}+1$$

Convert 1 to fraction \frac{12}{12}.

$$-\frac{41}{12}+\frac{12}{12}$$

Since -\frac{41}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{-41+12}{12}$$

Add -41 and 12 to get -29.

$$-\frac{29}{12}$$

Factor

$$-\frac{29}{12} = -2\frac{5}{12} = -2.4166666666666665$$