Solve 1/4[4/5-(8/3div2/9)]

$$\frac { 1 } { 4 } [ \frac { 4 } { 5 } - ( \frac { 8 } { 3 } \div \frac { 2 } { 9 } ) ]$$

Evaluate

$$-\frac{14}{5}=-2.8$$

Solution Steps

Divide \frac{8}{3} by \frac{2}{9} by multiplying \frac{8}{3} by the reciprocal of \frac{2}{9}.

$$\frac{1}{4}\left(\frac{4}{5}-\frac{8}{3}\times \frac{9}{2}\right)$$

Multiply \frac{8}{3} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}\left(\frac{4}{5}-\frac{8\times 9}{3\times 2}\right)$$

Do the multiplications in the fraction \frac{8\times 9}{3\times 2}.

$$\frac{1}{4}\left(\frac{4}{5}-\frac{72}{6}\right)$$

Divide 72 by 6 to get 12.

$$\frac{1}{4}\left(\frac{4}{5}-12\right)$$

Convert 12 to fraction \frac{60}{5}.

$$\frac{1}{4}\left(\frac{4}{5}-\frac{60}{5}\right)$$

Since \frac{4}{5} and \frac{60}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}\times \frac{4-60}{5}$$

Subtract 60 from 4 to get -56.

$$\frac{1}{4}\left(-\frac{56}{5}\right)$$

Multiply \frac{1}{4} times -\frac{56}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-56\right)}{4\times 5}$$

Do the multiplications in the fraction \frac{1\left(-56\right)}{4\times 5}.

$$\frac{-56}{20}$$

Reduce the fraction \frac{-56}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{14}{5}$$

Factor

$$-\frac{14}{5} = -2\frac{4}{5} = -2.8$$