Solve (11/2:2/3)*(23/4+6/8)=

$$( 1 \frac { 1 } { 2 } : \frac { 2 } { 3 } ) \times ( 2 \frac { 3 } { 4 } + \frac { 6 } { 8 } ) =$$

Evaluate

$$\frac{63}{8}=7.875$$

Solution Steps

Divide \frac{1\times 2+1}{2} by \frac{2}{3} by multiplying \frac{1\times 2+1}{2} by the reciprocal of \frac{2}{3}.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{3\times 3}{2\times 2}\left(\frac{2\times 4+3}{4}+\frac{6}{8}\right)$$

Multiply 3 and 3 to get 9.

$$\frac{9}{2\times 2}\left(\frac{2\times 4+3}{4}+\frac{6}{8}\right)$$

Multiply 2 and 2 to get 4.

$$\frac{9}{4}\left(\frac{2\times 4+3}{4}+\frac{6}{8}\right)$$

Multiply 2 and 4 to get 8.

$$\frac{9}{4}\left(\frac{8+3}{4}+\frac{6}{8}\right)$$

Add 8 and 3 to get 11.

$$\frac{9}{4}\left(\frac{11}{4}+\frac{6}{8}\right)$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}\left(\frac{11}{4}+\frac{3}{4}\right)$$

Since \frac{11}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{9}{4}\times \frac{11+3}{4}$$

Add 11 and 3 to get 14.

$$\frac{9}{4}\times \frac{14}{4}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{4}\times \frac{7}{2}$$

Multiply \frac{9}{4} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 7}{4\times 2}$$

Do the multiplications in the fraction \frac{9\times 7}{4\times 2}.

$$\frac{63}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 7}{2 ^ {3}} = 7\frac{7}{8} = 7.875$$