Solve 1/5xdiv2/5(1/2-1/4)-2frac{2}{3}div(-frac{2}{3})*(frac{1}{2})

$$\frac { 1 } { 5 } x \div \frac { 2 } { 5 } ( \frac { 1 } { 2 } - \frac { 1 } { 4 } ) - 2 \frac { 2 } { 3 } \div ( - \frac { 2 } { 3 } ) \times ( \frac { 1 } { 2 } )$$

Evaluate

$$\frac{x}{8}+2$$

Short Solution Steps

Divide \frac{1}{5}x by \frac{2}{5} by multiplying \frac{1}{5}x by the reciprocal of \frac{2}{5}.

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

Cancel out 5 and 5.

$$\frac{x}{2}\left(\frac{1}{2}-\frac{1}{4}\right)-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{x}{2}\left(\frac{2}{4}-\frac{1}{4}\right)-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{2}\times \frac{2-1}{4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Subtract 1 from 2 to get 1.

$$\frac{x}{2}\times \frac{1}{4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Multiply \frac{x}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{2\times 4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Divide \frac{2\times 3+2}{3} by -\frac{2}{3} by multiplying \frac{2\times 3+2}{3} by the reciprocal of -\frac{2}{3}.

$$\frac{x}{2\times 4}-\frac{\left(2\times 3+2\right)\times 3}{3\left(-2\right)}\times \frac{1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{x}{2\times 4}-\frac{2+2\times 3}{-2}\times \frac{1}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{x}{2\times 4}-\frac{2+6}{-2}\times \frac{1}{2}$$

Add 2 and 6 to get 8.

$$\frac{x}{2\times 4}-\frac{8}{-2}\times \frac{1}{2}$$

Divide 8 by -2 to get -4.

$$\frac{x}{2\times 4}-\left(-4\times \frac{1}{2}\right)$$

Multiply -4 and \frac{1}{2} to get \frac{-4}{2}.

$$\frac{x}{2\times 4}-\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$\frac{x}{2\times 4}-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{x}{2\times 4}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2\times 4}{2\times 4}.

$$\frac{x}{2\times 4}+\frac{2\times 2\times 4}{2\times 4}$$

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

$$\frac{x+2\times 2\times 4}{2\times 4}$$

Do the multiplications in x+2\times 2\times 4.

$$\frac{x+16}{2\times 4}$$

Expand 2\times 4.

$$\frac{x+16}{8}$$

Expand

$$\frac{x}{8}+2$$

Short Solution Steps

Divide \frac{1}{5}x by \frac{2}{5} by multiplying \frac{1}{5}x by the reciprocal of \frac{2}{5}.

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

Cancel out 5 and 5.

$$\frac{x}{2}\left(\frac{1}{2}-\frac{1}{4}\right)-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{x}{2}\left(\frac{2}{4}-\frac{1}{4}\right)-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{2}\times \frac{2-1}{4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Subtract 1 from 2 to get 1.

$$\frac{x}{2}\times \frac{1}{4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Multiply \frac{x}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{2\times 4}-\frac{\frac{2\times 3+2}{3}}{-\frac{2}{3}}\times \frac{1}{2}$$

Divide \frac{2\times 3+2}{3} by -\frac{2}{3} by multiplying \frac{2\times 3+2}{3} by the reciprocal of -\frac{2}{3}.

$$\frac{x}{2\times 4}-\frac{\left(2\times 3+2\right)\times 3}{3\left(-2\right)}\times \frac{1}{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{x}{2\times 4}-\frac{2+2\times 3}{-2}\times \frac{1}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{x}{2\times 4}-\frac{2+6}{-2}\times \frac{1}{2}$$

Add 2 and 6 to get 8.

$$\frac{x}{2\times 4}-\frac{8}{-2}\times \frac{1}{2}$$

Divide 8 by -2 to get -4.

$$\frac{x}{2\times 4}-\left(-4\times \frac{1}{2}\right)$$

Multiply -4 and \frac{1}{2} to get \frac{-4}{2}.

$$\frac{x}{2\times 4}-\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$\frac{x}{2\times 4}-\left(-2\right)$$

The opposite of -2 is 2.

$$\frac{x}{2\times 4}+2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2\times 4}{2\times 4}.

$$\frac{x}{2\times 4}+\frac{2\times 2\times 4}{2\times 4}$$

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

$$\frac{x+2\times 2\times 4}{2\times 4}$$

Do the multiplications in x+2\times 2\times 4.

$$\frac{x+16}{2\times 4}$$

Expand 2\times 4.

$$\frac{x+16}{8}$$