Solve 2/3+4/5-8/9+9/6divfrac{4}{3}

$$\frac { 2 } { 3 } + \frac { 4 } { 5 } - \frac { 8 } { 9 } + \frac { 9 } { 6 } \div \frac { 4 } { 3 }$$

Evaluate

$$\frac{613}{360}\approx 1.702777778$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{12}{15}-\frac{8}{9}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Since \frac{10}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+12}{15}-\frac{8}{9}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Add 10 and 12 to get 22.

$$\frac{22}{15}-\frac{8}{9}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Least common multiple of 15 and 9 is 45. Convert \frac{22}{15} and \frac{8}{9} to fractions with denominator 45.

$$\frac{66}{45}-\frac{40}{45}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Since \frac{66}{45} and \frac{40}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{66-40}{45}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Subtract 40 from 66 to get 26.

$$\frac{26}{45}+\frac{\frac{9}{6}}{\frac{4}{3}}$$

Divide \frac{9}{6} by \frac{4}{3} by multiplying \frac{9}{6} by the reciprocal of \frac{4}{3}.

$$\frac{26}{45}+\frac{9\times 3}{6\times 4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{26}{45}+\frac{3\times 3}{2\times 4}$$

Multiply 3 and 3 to get 9.

$$\frac{26}{45}+\frac{9}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{26}{45}+\frac{9}{8}$$

Least common multiple of 45 and 8 is 360. Convert \frac{26}{45} and \frac{9}{8} to fractions with denominator 360.

$$\frac{208}{360}+\frac{405}{360}$$

Since \frac{208}{360} and \frac{405}{360} have the same denominator, add them by adding their numerators.

$$\frac{208+405}{360}$$

Add 208 and 405 to get 613.

$$\frac{613}{360}$$

Factor

$$\frac{613}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 1\frac{253}{360} = 1.7027777777777777$$