Solve -1-(2*1/6)/4+(frac{1{4}div3/2)-9/2}-frac{3}{4}

$$- \frac { 1 - ( 2 \cdot \frac { 1 } { 6 } ) } { 4 + ( \frac { 1 } { 4 } \div \frac { 3 } { 2 } ) - \frac { 9 } { 2 } } - \frac { 3 } { 4 }$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$-\frac{1-\frac{2}{6}}{4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{9}{2}}-\frac{3}{4}$$

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

$$-\frac{1-\frac{1}{3}}{4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{9}{2}}-\frac{3}{4}$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{\frac{3}{3}-\frac{1}{3}}{4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{9}{2}}-\frac{3}{4}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{\frac{3-1}{3}}{4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{9}{2}}-\frac{3}{4}$$

Subtract 1 from 3 to get 2.

$$-\frac{\frac{2}{3}}{4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{9}{2}}-\frac{3}{4}$$

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

$$-\frac{\frac{2}{3}}{4+\frac{1}{4}\times \frac{2}{3}-\frac{9}{2}}-\frac{3}{4}$$

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{\frac{2}{3}}{4+\frac{1\times 2}{4\times 3}-\frac{9}{2}}-\frac{3}{4}$$

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

$$-\frac{\frac{2}{3}}{4+\frac{2}{12}-\frac{9}{2}}-\frac{3}{4}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{\frac{2}{3}}{4+\frac{1}{6}-\frac{9}{2}}-\frac{3}{4}$$

Convert 4 to fraction \frac{24}{6}.

$$-\frac{\frac{2}{3}}{\frac{24}{6}+\frac{1}{6}-\frac{9}{2}}-\frac{3}{4}$$

Since \frac{24}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$-\frac{\frac{2}{3}}{\frac{24+1}{6}-\frac{9}{2}}-\frac{3}{4}$$

Add 24 and 1 to get 25.

$$-\frac{\frac{2}{3}}{\frac{25}{6}-\frac{9}{2}}-\frac{3}{4}$$

Least common multiple of 6 and 2 is 6. Convert \frac{25}{6} and \frac{9}{2} to fractions with denominator 6.

$$-\frac{\frac{2}{3}}{\frac{25}{6}-\frac{27}{6}}-\frac{3}{4}$$

Since \frac{25}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{\frac{2}{3}}{\frac{25-27}{6}}-\frac{3}{4}$$

Subtract 27 from 25 to get -2.

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

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

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

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

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

Express \frac{2}{3}\left(-3\right) as a single fraction.

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

Multiply 2 and -3 to get -6.

$$-\frac{-6}{3}-\frac{3}{4}$$

Divide -6 by 3 to get -2.

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

The opposite of -2 is 2.

$$2-\frac{3}{4}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{8}{4}-\frac{3}{4}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-3}{4}$$

Subtract 3 from 8 to get 5.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$