Solve 1-1/2:2/frac{1{4}-3/2+1}-(frac{1/2-2)^3}{(1-frac{1}{4})^2}-frac{frac{frac{1}{2}-frac{1}{4}}{frac{3}{2}}}{frac{1}{frac{1}{6}-frac{5}{3}}}

$$\frac { 1 - \frac { 1 } { 2 } : 2 } { \frac { 1 } { 4 } - \frac { 3 } { 2 } + 1 } - \frac { ( \frac { 1 } { 2 } - 2 ) ^ { 3 } } { ( 1 - \frac { 1 } { 4 } ) ^ { 2 } } - \frac { \frac { \frac { 1 } { 2 } - \frac { 1 } { 4 } } { \frac { 3 } { 2 } } } { \frac { 1 } { \frac { 1 } { 6 } - \frac { 5 } { 3 } } }$$

Evaluate

$$\frac{13}{4}=3.25$$

Solution Steps

Express \frac{\frac{1}{2}}{2} as a single fraction.

$$\frac{1-\frac{1}{2\times 2}}{\frac{1}{4}-\frac{3}{2}+1}-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Multiply 2 and 2 to get 4.

$$\frac{1-\frac{1}{4}}{\frac{1}{4}-\frac{3}{2}+1}-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$\frac{\frac{3}{4}}{\frac{1}{4}-\frac{3}{2}+1}-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Subtract \frac{3}{2} from \frac{1}{4} to get -\frac{5}{4}.

$$\frac{\frac{3}{4}}{-\frac{5}{4}+1}-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Add -\frac{5}{4} and 1 to get -\frac{1}{4}.

$$\frac{\frac{3}{4}}{-\frac{1}{4}}-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Divide \frac{3}{4} by -\frac{1}{4} by multiplying \frac{3}{4} by the reciprocal of -\frac{1}{4}.

$$\frac{3}{4}\left(-4\right)-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Multiply \frac{3}{4} and -4 to get -3.

$$-3-\frac{\left(\frac{1}{2}-2\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$-3-\frac{\left(-\frac{3}{2}\right)^{3}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$-3-\frac{-\frac{27}{8}}{\left(1-\frac{1}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$-3-\frac{-\frac{27}{8}}{\left(\frac{3}{4}\right)^{2}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-3-\frac{-\frac{27}{8}}{\frac{9}{16}}-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Divide -\frac{27}{8} by \frac{9}{16} by multiplying -\frac{27}{8} by the reciprocal of \frac{9}{16}.

$$-3-\left(-\frac{27}{8}\times \frac{16}{9}\right)-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Multiply -\frac{27}{8} and \frac{16}{9} to get -6.

$$-3-\left(-6\right)-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

The opposite of -6 is 6.

$$-3+6-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Add -3 and 6 to get 3.

$$3-\frac{\frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}}}{\frac{1}{\frac{1}{6}-\frac{5}{3}}}$$

Divide \frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}} by \frac{1}{\frac{1}{6}-\frac{5}{3}} by multiplying \frac{\frac{1}{2}-\frac{1}{4}}{\frac{3}{2}} by the reciprocal of \frac{1}{\frac{1}{6}-\frac{5}{3}}.

$$3-\frac{\left(\frac{1}{2}-\frac{1}{4}\right)\left(\frac{1}{6}-\frac{5}{3}\right)}{\frac{3}{2}}$$

Subtract \frac{1}{4} from \frac{1}{2} to get \frac{1}{4}.

$$3-\frac{\frac{1}{4}\left(\frac{1}{6}-\frac{5}{3}\right)}{\frac{3}{2}}$$

Subtract \frac{5}{3} from \frac{1}{6} to get -\frac{3}{2}.

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

Multiply \frac{1}{4} and -\frac{3}{2} to get -\frac{3}{8}.

$$3-\frac{-\frac{3}{8}}{\frac{3}{2}}$$

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

$$3-\left(-\frac{3}{8}\times \frac{2}{3}\right)$$

Multiply -\frac{3}{8} and \frac{2}{3} to get -\frac{1}{4}.

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

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$3+\frac{1}{4}$$

Add 3 and \frac{1}{4} to get \frac{13}{4}.

$$\frac{13}{4}$$

Factor

$$\frac{13}{2 ^ {2}} = 3\frac{1}{4} = 3.25$$