Solve {l}{3-(4*3-5)-(2/3+4/5-3/2)}{-(12-5)-(2/5+4-3)}

$$\left. \begin{array} { l } { 3 - ( 4 \cdot 3 - 5 ) - ( \frac { 2 } { 3 } + \frac { 4 } { 5 } - \frac { 3 } { 2 } ) } \\ { - ( 12 - 5 ) - ( \frac { 2 } { 5 } + 4 - 3 ) } \end{array} \right.$$

Evaluate

$$-\frac{371}{30}\approx -12.366666667$$

Solution Steps

Multiply 4 and 3 to get 12.

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

Subtract 5 from 12 to get 7.

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

Subtract 7 from 3 to get -4.

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

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$-4-\left(\frac{10}{15}+\frac{12}{15}-\frac{3}{2}\right)-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$-4-\left(\frac{10+12}{15}-\frac{3}{2}\right)-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Add 10 and 12 to get 22.

$$-4-\left(\frac{22}{15}-\frac{3}{2}\right)-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Least common multiple of 15 and 2 is 30. Convert \frac{22}{15} and \frac{3}{2} to fractions with denominator 30.

$$-4-\left(\frac{44}{30}-\frac{45}{30}\right)-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Since \frac{44}{30} and \frac{45}{30} have the same denominator, subtract them by subtracting their numerators.

$$-4-\frac{44-45}{30}-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Subtract 45 from 44 to get -1.

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

The opposite of -\frac{1}{30} is \frac{1}{30}.

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

Convert -4 to fraction -\frac{120}{30}.

$$-\frac{120}{30}+\frac{1}{30}-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Since -\frac{120}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{-120+1}{30}-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Add -120 and 1 to get -119.

$$-\frac{119}{30}-\left(12-5\right)-\left(\frac{2}{5}+4-3\right)$$

Subtract 5 from 12 to get 7.

$$-\frac{119}{30}-7-\left(\frac{2}{5}+4-3\right)$$

Convert 7 to fraction \frac{210}{30}.

$$-\frac{119}{30}-\frac{210}{30}-\left(\frac{2}{5}+4-3\right)$$

Since -\frac{119}{30} and \frac{210}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-119-210}{30}-\left(\frac{2}{5}+4-3\right)$$

Subtract 210 from -119 to get -329.

$$-\frac{329}{30}-\left(\frac{2}{5}+4-3\right)$$

Convert 4 to fraction \frac{20}{5}.

$$-\frac{329}{30}-\left(\frac{2}{5}+\frac{20}{5}-3\right)$$

Since \frac{2}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.

$$-\frac{329}{30}-\left(\frac{2+20}{5}-3\right)$$

Add 2 and 20 to get 22.

$$-\frac{329}{30}-\left(\frac{22}{5}-3\right)$$

Convert 3 to fraction \frac{15}{5}.

$$-\frac{329}{30}-\left(\frac{22}{5}-\frac{15}{5}\right)$$

Since \frac{22}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{329}{30}-\frac{22-15}{5}$$

Subtract 15 from 22 to get 7.

$$-\frac{329}{30}-\frac{7}{5}$$

Least common multiple of 30 and 5 is 30. Convert -\frac{329}{30} and \frac{7}{5} to fractions with denominator 30.

$$-\frac{329}{30}-\frac{42}{30}$$

Since -\frac{329}{30} and \frac{42}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-329-42}{30}$$

Subtract 42 from -329 to get -371.

$$-\frac{371}{30}$$

Factor

$$-\frac{371}{30} = -12\frac{11}{30} = -12.366666666666667$$