Solve (87/2/9frac{8{3}}+16/2)

$$( \frac { 8 \frac { 7 } { 2 } } { 9 \frac { 8 } { 3 } } + \frac { 16 } { 2 } )$$

Evaluate

$$\frac{629}{70}\approx 8.985714286$$

Solution Steps

Divide \frac{8\times 2+7}{2} by \frac{9\times 3+8}{3} by multiplying \frac{8\times 2+7}{2} by the reciprocal of \frac{9\times 3+8}{3}.

$$\frac{\left(8\times 2+7\right)\times 3}{2\left(9\times 3+8\right)}+\frac{16}{2}$$

Multiply 8 and 2 to get 16.

$$\frac{\left(16+7\right)\times 3}{2\left(9\times 3+8\right)}+\frac{16}{2}$$

Add 16 and 7 to get 23.

$$\frac{23\times 3}{2\left(9\times 3+8\right)}+\frac{16}{2}$$

Multiply 23 and 3 to get 69.

$$\frac{69}{2\left(9\times 3+8\right)}+\frac{16}{2}$$

Multiply 9 and 3 to get 27.

$$\frac{69}{2\left(27+8\right)}+\frac{16}{2}$$

Add 27 and 8 to get 35.

$$\frac{69}{2\times 35}+\frac{16}{2}$$

Multiply 2 and 35 to get 70.

$$\frac{69}{70}+\frac{16}{2}$$

Divide 16 by 2 to get 8.

$$\frac{69}{70}+8$$

Convert 8 to fraction \frac{560}{70}.

$$\frac{69}{70}+\frac{560}{70}$$

Since \frac{69}{70} and \frac{560}{70} have the same denominator, add them by adding their numerators.

$$\frac{69+560}{70}$$

Add 69 and 560 to get 629.

$$\frac{629}{70}$$

Factor

$$\frac{17 \cdot 37}{2 \cdot 5 \cdot 7} = 8\frac{69}{70} = 8.985714285714286$$