Solve 4/5(2/3k-2/3)

$$\frac { 4 } { 5 } ( \frac { 2 } { 3 k } - \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{8}{15}+\frac{8}{15k}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3k and 3 is 3k. Multiply \frac{2}{3} times \frac{k}{k}.

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

Since \frac{2}{3k} and \frac{2k}{3k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}\times \frac{2-2k}{3k}$$

Multiply \frac{4}{5} times \frac{2-2k}{3k} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(2-2k\right)}{5\times 3k}$$

Multiply 5 and 3 to get 15.

$$\frac{4\left(2-2k\right)}{15k}$$

Use the distributive property to multiply 4 by 2-2k.

$$\frac{8-8k}{15k}$$

Expand

$$-\frac{8}{15}+\frac{8}{15k}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3k and 3 is 3k. Multiply \frac{2}{3} times \frac{k}{k}.

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

Since \frac{2}{3k} and \frac{2k}{3k} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}\times \frac{2-2k}{3k}$$

Multiply \frac{4}{5} times \frac{2-2k}{3k} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(2-2k\right)}{5\times 3k}$$

Multiply 5 and 3 to get 15.

$$\frac{4\left(2-2k\right)}{15k}$$

Use the distributive property to multiply 4 by 2-2k.

$$\frac{8-8k}{15k}$$