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

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

Evaluate

$$-\frac{44}{15}\approx -2.933333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{4}{3} to fractions with denominator 15.

$$\frac{3}{15}+\frac{20}{15}-3-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Since \frac{3}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\frac{3+20}{15}-3-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Add 3 and 20 to get 23.

$$\frac{23}{15}-3-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Convert 3 to fraction \frac{45}{15}.

$$\frac{23}{15}-\frac{45}{15}-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Since \frac{23}{15} and \frac{45}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-45}{15}-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Subtract 45 from 23 to get -22.

$$-\frac{22}{15}-\left(-\frac{1}{5}-\frac{4}{3}+3\right)$$

Least common multiple of 5 and 3 is 15. Convert -\frac{1}{5} and \frac{4}{3} to fractions with denominator 15.

$$-\frac{22}{15}-\left(-\frac{3}{15}-\frac{20}{15}+3\right)$$

Since -\frac{3}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{22}{15}-\left(\frac{-3-20}{15}+3\right)$$

Subtract 20 from -3 to get -23.

$$-\frac{22}{15}-\left(-\frac{23}{15}+3\right)$$

Convert 3 to fraction \frac{45}{15}.

$$-\frac{22}{15}-\left(-\frac{23}{15}+\frac{45}{15}\right)$$

Since -\frac{23}{15} and \frac{45}{15} have the same denominator, add them by adding their numerators.

$$-\frac{22}{15}-\frac{-23+45}{15}$$

Add -23 and 45 to get 22.

$$-\frac{22}{15}-\frac{22}{15}$$

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

$$\frac{-22-22}{15}$$

Subtract 22 from -22 to get -44.

$$-\frac{44}{15}$$

Factor

$$-\frac{44}{15} = -2\frac{14}{15} = -2.933333333333333$$