Solve -4/6(2/4j+2/7)

$$- \frac { 4 } { 6 } ( \frac { 2 } { 4 j } + \frac { 2 } { 7 } )$$

Evaluate

$$-\frac{4}{21}-\frac{1}{3j}$$

Short Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4j and 7 is 28j. Multiply \frac{2}{4j} times \frac{7}{7}. Multiply \frac{2}{7} times \frac{4j}{4j}.

$$-\frac{2}{3}\left(\frac{2\times 7}{28j}+\frac{2\times 4j}{28j}\right)$$

Since \frac{2\times 7}{28j} and \frac{2\times 4j}{28j} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}\times \frac{2\times 7+2\times 4j}{28j}$$

Do the multiplications in 2\times 7+2\times 4j.

$$-\frac{2}{3}\times \frac{14+8j}{28j}$$

Factor the expressions that are not already factored in \frac{14+8j}{28j}.

$$-\frac{2}{3}\times \frac{2\left(4j+7\right)}{28j}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{2}{3}\times \frac{4j+7}{14j}$$

Multiply -\frac{2}{3} times \frac{4j+7}{14j} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(4j+7\right)}{3\times 14j}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(4j+7\right)}{3\times 7j}$$

Multiply 3 and 7 to get 21.

$$\frac{-\left(4j+7\right)}{21j}$$

Cancel out -1 in both numerator and denominator.

$$\frac{4j+7}{-21j}$$

Expand

$$-\frac{4}{21}-\frac{1}{3j}$$

Short Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4j and 7 is 28j. Multiply \frac{2}{4j} times \frac{7}{7}. Multiply \frac{2}{7} times \frac{4j}{4j}.

$$-\frac{2}{3}\left(\frac{2\times 7}{28j}+\frac{2\times 4j}{28j}\right)$$

Since \frac{2\times 7}{28j} and \frac{2\times 4j}{28j} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}\times \frac{2\times 7+2\times 4j}{28j}$$

Do the multiplications in 2\times 7+2\times 4j.

$$-\frac{2}{3}\times \frac{14+8j}{28j}$$

Factor the expressions that are not already factored in \frac{14+8j}{28j}.

$$-\frac{2}{3}\times \frac{2\left(4j+7\right)}{28j}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{2}{3}\times \frac{4j+7}{14j}$$

Multiply -\frac{2}{3} times \frac{4j+7}{14j} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(4j+7\right)}{3\times 14j}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-\left(4j+7\right)}{3\times 7j}$$

Multiply 3 and 7 to get 21.

$$\frac{-\left(4j+7\right)}{21j}$$

Cancel out -1 in both numerator and denominator.

$$\frac{4j+7}{-21j}$$