Solve [2/3(1/4x-2/3)]div(1/2+frac{2}{3})

$$[ \frac { 2 } { 3 } ( \frac { 1 } { 4 } x - \frac { 2 } { 3 } ) ] \div ( \frac { 1 } { 2 } + \frac { 2 } { 3 } )$$

Evaluate

$$\frac{x}{7}-\frac{8}{21}$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{3}{6}+\frac{4}{6}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{3+4}{6}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{7}{6}}$$

Divide \frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right) by \frac{7}{6} to get \frac{4}{7}\left(\frac{1}{4}x-\frac{2}{3}\right).

$$\frac{4}{7}\left(\frac{1}{4}x-\frac{2}{3}\right)$$

Use the distributive property to multiply \frac{4}{7} by \frac{1}{4}x-\frac{2}{3}.

$$\frac{4}{7}\times \frac{1}{4}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

Multiply \frac{4}{7} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{7\times 4}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{1}{7}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

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

$$\frac{1}{7}x+\frac{4\left(-2\right)}{7\times 3}$$

Do the multiplications in the fraction \frac{4\left(-2\right)}{7\times 3}.

$$\frac{1}{7}x+\frac{-8}{21}$$

Fraction \frac{-8}{21} can be rewritten as -\frac{8}{21} by extracting the negative sign.

$$\frac{1}{7}x-\frac{8}{21}$$

Expand

$$\frac{x}{7}-\frac{8}{21}$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{3}{6}+\frac{4}{6}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{3+4}{6}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right)}{\frac{7}{6}}$$

Divide \frac{2}{3}\left(\frac{1}{4}x-\frac{2}{3}\right) by \frac{7}{6} to get \frac{4}{7}\left(\frac{1}{4}x-\frac{2}{3}\right).

$$\frac{4}{7}\left(\frac{1}{4}x-\frac{2}{3}\right)$$

Use the distributive property to multiply \frac{4}{7} by \frac{1}{4}x-\frac{2}{3}.

$$\frac{4}{7}\times \frac{1}{4}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

Multiply \frac{4}{7} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{7\times 4}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{1}{7}x+\frac{4}{7}\left(-\frac{2}{3}\right)$$

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

$$\frac{1}{7}x+\frac{4\left(-2\right)}{7\times 3}$$

Do the multiplications in the fraction \frac{4\left(-2\right)}{7\times 3}.

$$\frac{1}{7}x+\frac{-8}{21}$$

Fraction \frac{-8}{21} can be rewritten as -\frac{8}{21} by extracting the negative sign.

$$\frac{1}{7}x-\frac{8}{21}$$