Solve 121/9-102/5/38frac{1{2}}+29/518

$$\frac{ 12 \frac{ 1 }{ 9 } -10 \frac{ 2 }{ 5 } }{ 38 \frac{ 1 }{ 2 } } +2 \frac{ 9 }{ 5 } 18$$

Evaluate

$$\frac{616}{9}\approx 68.444444444$$

Solution Steps

Multiply 12 and 9 to get 108.

$$\frac{\frac{108+1}{9}-\frac{10\times 5+2}{5}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Add 108 and 1 to get 109.

$$\frac{\frac{109}{9}-\frac{10\times 5+2}{5}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Multiply 10 and 5 to get 50.

$$\frac{\frac{109}{9}-\frac{50+2}{5}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Add 50 and 2 to get 52.

$$\frac{\frac{109}{9}-\frac{52}{5}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Least common multiple of 9 and 5 is 45. Convert \frac{109}{9} and \frac{52}{5} to fractions with denominator 45.

$$\frac{\frac{545}{45}-\frac{468}{45}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Since \frac{545}{45} and \frac{468}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{545-468}{45}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Subtract 468 from 545 to get 77.

$$\frac{\frac{77}{45}}{\frac{38\times 2+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Multiply 38 and 2 to get 76.

$$\frac{\frac{77}{45}}{\frac{76+1}{2}}+\frac{2\times 5+9}{5}\times 18$$

Add 76 and 1 to get 77.

$$\frac{\frac{77}{45}}{\frac{77}{2}}+\frac{2\times 5+9}{5}\times 18$$

Divide \frac{77}{45} by \frac{77}{2} by multiplying \frac{77}{45} by the reciprocal of \frac{77}{2}.

$$\frac{77}{45}\times \frac{2}{77}+\frac{2\times 5+9}{5}\times 18$$

Multiply \frac{77}{45} times \frac{2}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{77\times 2}{45\times 77}+\frac{2\times 5+9}{5}\times 18$$

Cancel out 77 in both numerator and denominator.

$$\frac{2}{45}+\frac{2\times 5+9}{5}\times 18$$

Multiply 2 and 5 to get 10.

$$\frac{2}{45}+\frac{10+9}{5}\times 18$$

Add 10 and 9 to get 19.

$$\frac{2}{45}+\frac{19}{5}\times 18$$

Express \frac{19}{5}\times 18 as a single fraction.

$$\frac{2}{45}+\frac{19\times 18}{5}$$

Multiply 19 and 18 to get 342.

$$\frac{2}{45}+\frac{342}{5}$$

Least common multiple of 45 and 5 is 45. Convert \frac{2}{45} and \frac{342}{5} to fractions with denominator 45.

$$\frac{2}{45}+\frac{3078}{45}$$

Since \frac{2}{45} and \frac{3078}{45} have the same denominator, add them by adding their numerators.

$$\frac{2+3078}{45}$$

Add 2 and 3078 to get 3080.

$$\frac{3080}{45}$$

Reduce the fraction \frac{3080}{45} to lowest terms by extracting and canceling out 5.

$$\frac{616}{9}$$

Factor

$$\frac{2 ^ {3} \cdot 7 \cdot 11}{3 ^ {2}} = 68\frac{4}{9} = 68.44444444444444$$