Solve (3/8+1/4)-(5/2+frac{3/6)}{frac{8}{7}(frac{1}{4})^2}=

$$\frac { ( \frac { 3 } { 8 } + \frac { 1 } { 4 } ) - ( \frac { 5 } { 2 } + \frac { 3 } { 6 } ) } { \frac { 8 } { 7 } ( \frac { 1 } { 4 } ) ^ { 2 } } =$$

Evaluate

$$-\frac{133}{4}=-33.25$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{3}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{3}{8}+\frac{2}{8}-\left(\frac{5}{2}+\frac{3}{6}\right)}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Since \frac{3}{8} and \frac{2}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{8}-\left(\frac{5}{2}+\frac{3}{6}\right)}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{8}-\left(\frac{5}{2}+\frac{3}{6}\right)}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{5}{8}-\left(\frac{5}{2}+\frac{1}{2}\right)}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Since \frac{5}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{8}-\frac{5+1}{2}}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{5}{8}-\frac{6}{2}}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Divide 6 by 2 to get 3.

$$\frac{\frac{5}{8}-3}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Convert 3 to fraction \frac{24}{8}.

$$\frac{\frac{5}{8}-\frac{24}{8}}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Since \frac{5}{8} and \frac{24}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-24}{8}}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Subtract 24 from 5 to get -19.

$$\frac{-\frac{19}{8}}{\frac{8}{7}\times \left(\frac{1}{4}\right)^{2}}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{-\frac{19}{8}}{\frac{8}{7}\times \frac{1}{16}}$$

Multiply \frac{8}{7} times \frac{1}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{19}{8}}{\frac{8\times 1}{7\times 16}}$$

Do the multiplications in the fraction \frac{8\times 1}{7\times 16}.

$$\frac{-\frac{19}{8}}{\frac{8}{112}}$$

Reduce the fraction \frac{8}{112} to lowest terms by extracting and canceling out 8.

$$\frac{-\frac{19}{8}}{\frac{1}{14}}$$

Divide -\frac{19}{8} by \frac{1}{14} by multiplying -\frac{19}{8} by the reciprocal of \frac{1}{14}.

$$-\frac{19}{8}\times 14$$

Express -\frac{19}{8}\times 14 as a single fraction.

$$\frac{-19\times 14}{8}$$

Multiply -19 and 14 to get -266.

$$\frac{-266}{8}$$

Reduce the fraction \frac{-266}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{133}{4}$$

Factor

$$-\frac{133}{4} = -33\frac{1}{4} = -33.25$$