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

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

Evaluate

$$-\frac{654}{2635}\approx -0.248197343$$

Solution Steps

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

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

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

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

Add 3 and 4 to get 7.

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

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

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

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

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

Subtract 10 from 119 to get 109.

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

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

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

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

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

Add 8 and 3 to get 11.

$$\frac{\frac{109}{85}}{\frac{11}{6}-\frac{21}{3}}$$

Divide 21 by 3 to get 7.

$$\frac{\frac{109}{85}}{\frac{11}{6}-7}$$

Convert 7 to fraction \frac{42}{6}.

$$\frac{\frac{109}{85}}{\frac{11}{6}-\frac{42}{6}}$$

Since \frac{11}{6} and \frac{42}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{109}{85}}{\frac{11-42}{6}}$$

Subtract 42 from 11 to get -31.

$$\frac{\frac{109}{85}}{-\frac{31}{6}}$$

Divide \frac{109}{85} by -\frac{31}{6} by multiplying \frac{109}{85} by the reciprocal of -\frac{31}{6}.

$$\frac{109}{85}\left(-\frac{6}{31}\right)$$

Multiply \frac{109}{85} times -\frac{6}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{109\left(-6\right)}{85\times 31}$$

Do the multiplications in the fraction \frac{109\left(-6\right)}{85\times 31}.

$$\frac{-654}{2635}$$

Fraction \frac{-654}{2635} can be rewritten as -\frac{654}{2635} by extracting the negative sign.

$$-\frac{654}{2635}$$

Factor

$$-\frac{654}{2635} = -0.24819734345351044$$