Solve 6/5[2/3+1/2]+1/2[frac{2}{5}+frac{5}{6}]-4(-3+6)

$$\frac { 6 } { 5 } [ \frac { 2 } { 3 } + \frac { 1 } { 2 } ] + \frac { 1 } { 2 } [ \frac { 2 } { 5 } + \frac { 5 } { 6 } ] - 4 ( - 3 + 6 )$$

Evaluate

$$-\frac{599}{60}\approx -9.983333333$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

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

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

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

Add 4 and 3 to get 7.

$$\frac{6}{5}\times \frac{7}{6}+\frac{1}{2}\left(\frac{2}{5}+\frac{5}{6}\right)-4\left(-3+6\right)$$

Multiply \frac{6}{5} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 7}{5\times 6}+\frac{1}{2}\left(\frac{2}{5}+\frac{5}{6}\right)-4\left(-3+6\right)$$

Cancel out 6 in both numerator and denominator.

$$\frac{7}{5}+\frac{1}{2}\left(\frac{2}{5}+\frac{5}{6}\right)-4\left(-3+6\right)$$

Least common multiple of 5 and 6 is 30. Convert \frac{2}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{7}{5}+\frac{1}{2}\left(\frac{12}{30}+\frac{25}{30}\right)-4\left(-3+6\right)$$

Since \frac{12}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$\frac{7}{5}+\frac{1}{2}\times \frac{12+25}{30}-4\left(-3+6\right)$$

Add 12 and 25 to get 37.

$$\frac{7}{5}+\frac{1}{2}\times \frac{37}{30}-4\left(-3+6\right)$$

Multiply \frac{1}{2} times \frac{37}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}+\frac{1\times 37}{2\times 30}-4\left(-3+6\right)$$

Do the multiplications in the fraction \frac{1\times 37}{2\times 30}.

$$\frac{7}{5}+\frac{37}{60}-4\left(-3+6\right)$$

Least common multiple of 5 and 60 is 60. Convert \frac{7}{5} and \frac{37}{60} to fractions with denominator 60.

$$\frac{84}{60}+\frac{37}{60}-4\left(-3+6\right)$$

Since \frac{84}{60} and \frac{37}{60} have the same denominator, add them by adding their numerators.

$$\frac{84+37}{60}-4\left(-3+6\right)$$

Add 84 and 37 to get 121.

$$\frac{121}{60}-4\left(-3+6\right)$$

Add -3 and 6 to get 3.

$$\frac{121}{60}-4\times 3$$

Multiply 4 and 3 to get 12.

$$\frac{121}{60}-12$$

Convert 12 to fraction \frac{720}{60}.

$$\frac{121}{60}-\frac{720}{60}$$

Since \frac{121}{60} and \frac{720}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-720}{60}$$

Subtract 720 from 121 to get -599.

$$-\frac{599}{60}$$

Factor

$$-\frac{599}{60} = -9\frac{59}{60} = -9.983333333333333$$