Solve (81/2/9frac{2{3}}+161/4/2)

$$( \frac { 8 \frac { 1 } { 2 } } { 9 \frac { 2 } { 3 } } + \frac { 16 \frac { 1 } { 4 } } { 2 } )$$

Evaluate

$$\frac{2089}{232}\approx 9.004310345$$

Solution Steps

Divide \frac{8\times 2+1}{2} by \frac{9\times 3+2}{3} by multiplying \frac{8\times 2+1}{2} by the reciprocal of \frac{9\times 3+2}{3}.

$$\frac{\left(8\times 2+1\right)\times 3}{2\left(9\times 3+2\right)}+\frac{\frac{16\times 4+1}{4}}{2}$$

Multiply 8 and 2 to get 16.

$$\frac{\left(16+1\right)\times 3}{2\left(9\times 3+2\right)}+\frac{\frac{16\times 4+1}{4}}{2}$$

Add 16 and 1 to get 17.

$$\frac{17\times 3}{2\left(9\times 3+2\right)}+\frac{\frac{16\times 4+1}{4}}{2}$$

Multiply 17 and 3 to get 51.

$$\frac{51}{2\left(9\times 3+2\right)}+\frac{\frac{16\times 4+1}{4}}{2}$$

Multiply 9 and 3 to get 27.

$$\frac{51}{2\left(27+2\right)}+\frac{\frac{16\times 4+1}{4}}{2}$$

Add 27 and 2 to get 29.

$$\frac{51}{2\times 29}+\frac{\frac{16\times 4+1}{4}}{2}$$

Multiply 2 and 29 to get 58.

$$\frac{51}{58}+\frac{\frac{16\times 4+1}{4}}{2}$$

Express \frac{\frac{16\times 4+1}{4}}{2} as a single fraction.

$$\frac{51}{58}+\frac{16\times 4+1}{4\times 2}$$

Multiply 16 and 4 to get 64.

$$\frac{51}{58}+\frac{64+1}{4\times 2}$$

Add 64 and 1 to get 65.

$$\frac{51}{58}+\frac{65}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{51}{58}+\frac{65}{8}$$

Least common multiple of 58 and 8 is 232. Convert \frac{51}{58} and \frac{65}{8} to fractions with denominator 232.

$$\frac{204}{232}+\frac{1885}{232}$$

Since \frac{204}{232} and \frac{1885}{232} have the same denominator, add them by adding their numerators.

$$\frac{204+1885}{232}$$

Add 204 and 1885 to get 2089.

$$\frac{2089}{232}$$

Factor

$$\frac{2089}{2 ^ {3} \cdot 29} = 9\frac{1}{232} = 9.004310344827585$$