Solve (2+3/4:9/8)*9/2-7/2]:frac{17}{4}-frac{6}{5}

$$( 2 + \frac { 3 } { 4 } : \frac { 9 } { 8 } ) \times \frac { 9 } { 2 } - \frac { 7 } { 2 } ] : \frac { 17 } { 4 } - \frac { 6 } { 5 }$$

Evaluate

$$\frac{17}{2}=8.5$$

Solution Steps

Divide \frac{3}{4} by \frac{9}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{8}.

$$\left(2+\frac{3}{4}\times \frac{8}{9}\right)\times \frac{9}{2}-\frac{7}{2}$$

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\left(2+\frac{3\times 8}{4\times 9}\right)\times \frac{9}{2}-\frac{7}{2}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\left(2+\frac{24}{36}\right)\times \frac{9}{2}-\frac{7}{2}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\left(2+\frac{2}{3}\right)\times \frac{9}{2}-\frac{7}{2}$$

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

$$\left(\frac{6}{3}+\frac{2}{3}\right)\times \frac{9}{2}-\frac{7}{2}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+2}{3}\times \frac{9}{2}-\frac{7}{2}$$

Add 6 and 2 to get 8.

$$\frac{8}{3}\times \frac{9}{2}-\frac{7}{2}$$

Multiply \frac{8}{3} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 9}{3\times 2}-\frac{7}{2}$$

Do the multiplications in the fraction \frac{8\times 9}{3\times 2}.

$$\frac{72}{6}-\frac{7}{2}$$

Divide 72 by 6 to get 12.

$$12-\frac{7}{2}$$

Convert 12 to fraction \frac{24}{2}.

$$\frac{24}{2}-\frac{7}{2}$$

Since \frac{24}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-7}{2}$$

Subtract 7 from 24 to get 17.

$$\frac{17}{2}$$

Factor

$$\frac{17}{2} = 8\frac{1}{2} = 8.5$$