Solve 5/3(3/1-4/1)+5/3(-frac{3}{1}-frac{3}{1})

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

Evaluate

$$-\frac{35}{3}\approx -11.666666667$$

Solution Steps

Anything divided by one gives itself.

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

Anything divided by one gives itself.

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

Subtract 4 from 3 to get -1.

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

Multiply \frac{5}{3} and -1 to get -\frac{5}{3}.

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

Anything divided by one gives itself.

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

Anything divided by one gives itself.

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

Subtract 3 from -3 to get -6.

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

Express \frac{5}{3}\left(-6\right) as a single fraction.

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

Multiply 5 and -6 to get -30.

$$-\frac{5}{3}+\frac{-30}{3}$$

Divide -30 by 3 to get -10.

$$-\frac{5}{3}-10$$

Convert 10 to fraction \frac{30}{3}.

$$-\frac{5}{3}-\frac{30}{3}$$

Since -\frac{5}{3} and \frac{30}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-30}{3}$$

Subtract 30 from -5 to get -35.

$$-\frac{35}{3}$$

Factor

$$-\frac{35}{3} = -11\frac{2}{3} = -11.666666666666666$$