Solve [3/4+5/2/(frac{3{4})(4/2)}]frac{5}{8}-7

$$[ \frac { \frac { 3 } { 4 } + \frac { 5 } { 2 } } { ( \frac { 3 } { 4 } ) ( \frac { 4 } { 2 } ) } ] \frac { 5 } { 8 } - 7$$

Evaluate

$$-\frac{271}{48}\approx -5.645833333$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{\frac{3}{4}+\frac{10}{4}}{\frac{3}{4}\times \frac{4}{2}}\times \frac{5}{8}-7$$

Since \frac{3}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+10}{4}}{\frac{3}{4}\times \frac{4}{2}}\times \frac{5}{8}-7$$

Add 3 and 10 to get 13.

$$\frac{\frac{13}{4}}{\frac{3}{4}\times \frac{4}{2}}\times \frac{5}{8}-7$$

Divide 4 by 2 to get 2.

$$\frac{\frac{13}{4}}{\frac{3}{4}\times 2}\times \frac{5}{8}-7$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{\frac{13}{4}}{\frac{3\times 2}{4}}\times \frac{5}{8}-7$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{13}{4}}{\frac{6}{4}}\times \frac{5}{8}-7$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{13}{4}}{\frac{3}{2}}\times \frac{5}{8}-7$$

Divide \frac{13}{4} by \frac{3}{2} by multiplying \frac{13}{4} by the reciprocal of \frac{3}{2}.

$$\frac{13}{4}\times \frac{2}{3}\times \frac{5}{8}-7$$

Multiply \frac{13}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 2}{4\times 3}\times \frac{5}{8}-7$$

Do the multiplications in the fraction \frac{13\times 2}{4\times 3}.

$$\frac{26}{12}\times \frac{5}{8}-7$$

Reduce the fraction \frac{26}{12} to lowest terms by extracting and canceling out 2.

$$\frac{13}{6}\times \frac{5}{8}-7$$

Multiply \frac{13}{6} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 5}{6\times 8}-7$$

Do the multiplications in the fraction \frac{13\times 5}{6\times 8}.

$$\frac{65}{48}-7$$

Convert 7 to fraction \frac{336}{48}.

$$\frac{65}{48}-\frac{336}{48}$$

Since \frac{65}{48} and \frac{336}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-336}{48}$$

Subtract 336 from 65 to get -271.

$$-\frac{271}{48}$$

Factor

$$-\frac{271}{48} = -5\frac{31}{48} = -5.645833333333333$$