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

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

Evaluate

$$-22$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

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

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Least common multiple of 4 and 8 is 8. Convert \frac{5}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{10}{8}-\frac{5}{8}}{\frac{\left(\frac{1}{4}\right)^{2}}{\frac{1}{5}-\frac{3}{4}}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Since \frac{10}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-5}{8}}{\frac{\left(\frac{1}{4}\right)^{2}}{\frac{1}{5}-\frac{3}{4}}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Subtract 5 from 10 to get 5.

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

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

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

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{\frac{5}{8}}{\frac{\frac{1}{16}}{\frac{4}{20}-\frac{15}{20}}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Since \frac{4}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{8}}{\frac{\frac{1}{16}}{\frac{4-15}{20}}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Subtract 15 from 4 to get -11.

$$\frac{\frac{5}{8}}{\frac{\frac{1}{16}}{-\frac{11}{20}}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Divide \frac{1}{16} by -\frac{11}{20} by multiplying \frac{1}{16} by the reciprocal of -\frac{11}{20}.

$$\frac{\frac{5}{8}}{\frac{1}{16}\left(-\frac{20}{11}\right)}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Multiply \frac{1}{16} times -\frac{20}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{8}}{\frac{1\left(-20\right)}{16\times 11}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Do the multiplications in the fraction \frac{1\left(-20\right)}{16\times 11}.

$$\frac{\frac{5}{8}}{\frac{-20}{176}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Reduce the fraction \frac{-20}{176} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5}{8}}{-\frac{5}{44}}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Divide \frac{5}{8} by -\frac{5}{44} by multiplying \frac{5}{8} by the reciprocal of -\frac{5}{44}.

$$\frac{5}{8}\left(-\frac{44}{5}\right)\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Multiply \frac{5}{8} times -\frac{44}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-44\right)}{8\times 5}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{-44}{8}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Reduce the fraction \frac{-44}{8} to lowest terms by extracting and canceling out 4.

$$-\frac{11}{2}\left(\frac{3}{2}+\frac{2\times 2+1}{2}\right)$$

Multiply 2 and 2 to get 4.

$$-\frac{11}{2}\left(\frac{3}{2}+\frac{4+1}{2}\right)$$

Add 4 and 1 to get 5.

$$-\frac{11}{2}\left(\frac{3}{2}+\frac{5}{2}\right)$$

Since \frac{3}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$-\frac{11}{2}\times \frac{3+5}{2}$$

Add 3 and 5 to get 8.

$$-\frac{11}{2}\times \frac{8}{2}$$

Divide 8 by 2 to get 4.

$$-\frac{11}{2}\times 4$$

Express -\frac{11}{2}\times 4 as a single fraction.

$$\frac{-11\times 4}{2}$$

Multiply -11 and 4 to get -44.

$$\frac{-44}{2}$$

Divide -44 by 2 to get -22.

$$-22$$

Factor

$$-22$$