Solve (3-1/2)+(1-1/2)/(4-frac{1{4})-(3/4-1)}

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

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

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

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

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

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{5}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 5 and 2 to get 7.

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

Since \frac{7}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 7 to get 6.

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

Divide 6 by 2 to get 3.

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

Convert 4 to fraction \frac{16}{4}.

$$\frac{3}{\frac{16}{4}-\frac{1}{4}-\left(\frac{3}{4}-1\right)}$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{\frac{16-1}{4}-\left(\frac{3}{4}-1\right)}$$

Subtract 1 from 16 to get 15.

$$\frac{3}{\frac{15}{4}-\left(\frac{3}{4}-1\right)}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{3}{\frac{15}{4}-\left(\frac{3}{4}-\frac{4}{4}\right)}$$

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

$$\frac{3}{\frac{15}{4}-\frac{3-4}{4}}$$

Subtract 4 from 3 to get -1.

$$\frac{3}{\frac{15}{4}-\left(-\frac{1}{4}\right)}$$

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

$$\frac{3}{\frac{15}{4}+\frac{1}{4}}$$

Since \frac{15}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{15+1}{4}}$$

Add 15 and 1 to get 16.

$$\frac{3}{\frac{16}{4}}$$

Divide 16 by 4 to get 4.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$