Solve (3/5+8/10-2/17)div(4/3+frac{1}{2}+(-frac{21}{6}))

$$( \frac{ 3 }{ 5 } + \frac{ 8 }{ 10 } - \frac{ 2 }{ 17 } ) \div ( \frac{ 4 }{ 3 } + \frac{ 1 }{ 2 } +(- \frac{ 21 }{ 6 } ))$$

Evaluate

$$-\frac{327}{425}\approx -0.769411765$$

Solution Steps

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{5}+\frac{4}{5}-\frac{2}{17}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Since \frac{3}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+4}{5}-\frac{2}{17}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{7}{5}-\frac{2}{17}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Least common multiple of 5 and 17 is 85. Convert \frac{7}{5} and \frac{2}{17} to fractions with denominator 85.

$$\frac{\frac{119}{85}-\frac{10}{85}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Since \frac{119}{85} and \frac{10}{85} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{119-10}{85}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Subtract 10 from 119 to get 109.

$$\frac{\frac{109}{85}}{\frac{4}{3}+\frac{1}{2}-\frac{21}{6}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{109}{85}}{\frac{8}{6}+\frac{3}{6}-\frac{21}{6}}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{109}{85}}{\frac{8+3}{6}-\frac{21}{6}}$$

Add 8 and 3 to get 11.

$$\frac{\frac{109}{85}}{\frac{11}{6}-\frac{21}{6}}$$

Since \frac{11}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{109}{85}}{\frac{11-21}{6}}$$

Subtract 21 from 11 to get -10.

$$\frac{\frac{109}{85}}{\frac{-10}{6}}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{109}{85}}{-\frac{5}{3}}$$

Divide \frac{109}{85} by -\frac{5}{3} by multiplying \frac{109}{85} by the reciprocal of -\frac{5}{3}.

$$\frac{109}{85}\left(-\frac{3}{5}\right)$$

Multiply \frac{109}{85} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{109\left(-3\right)}{85\times 5}$$

Do the multiplications in the fraction \frac{109\left(-3\right)}{85\times 5}.

$$\frac{-327}{425}$$

Fraction \frac{-327}{425} can be rewritten as -\frac{327}{425} by extracting the negative sign.

$$-\frac{327}{425}$$

Factor

$$-\frac{327}{425} = -0.7694117647058824$$