Solve 8/7+-6/11+-8/21+8/22=

$$\frac{ 8 }{ 7 } + \frac{ -6 }{ 11 } + \frac{ -8 }{ 21 } + \frac{ 8 }{ 22 } =$$

Evaluate

$$\frac{134}{231}\approx 0.58008658$$

Solution Steps

Fraction \frac{-6}{11} can be rewritten as -\frac{6}{11} by extracting the negative sign.

$$\frac{8}{7}-\frac{6}{11}+\frac{-8}{21}+\frac{8}{22}$$

Least common multiple of 7 and 11 is 77. Convert \frac{8}{7} and \frac{6}{11} to fractions with denominator 77.

$$\frac{88}{77}-\frac{42}{77}+\frac{-8}{21}+\frac{8}{22}$$

Since \frac{88}{77} and \frac{42}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{88-42}{77}+\frac{-8}{21}+\frac{8}{22}$$

Subtract 42 from 88 to get 46.

$$\frac{46}{77}+\frac{-8}{21}+\frac{8}{22}$$

Fraction \frac{-8}{21} can be rewritten as -\frac{8}{21} by extracting the negative sign.

$$\frac{46}{77}-\frac{8}{21}+\frac{8}{22}$$

Least common multiple of 77 and 21 is 231. Convert \frac{46}{77} and \frac{8}{21} to fractions with denominator 231.

$$\frac{138}{231}-\frac{88}{231}+\frac{8}{22}$$

Since \frac{138}{231} and \frac{88}{231} have the same denominator, subtract them by subtracting their numerators.

$$\frac{138-88}{231}+\frac{8}{22}$$

Subtract 88 from 138 to get 50.

$$\frac{50}{231}+\frac{8}{22}$$

Reduce the fraction \frac{8}{22} to lowest terms by extracting and canceling out 2.

$$\frac{50}{231}+\frac{4}{11}$$

Least common multiple of 231 and 11 is 231. Convert \frac{50}{231} and \frac{4}{11} to fractions with denominator 231.

$$\frac{50}{231}+\frac{84}{231}$$

Since \frac{50}{231} and \frac{84}{231} have the same denominator, add them by adding their numerators.

$$\frac{50+84}{231}$$

Add 50 and 84 to get 134.

$$\frac{134}{231}$$

Factor

$$\frac{2 \cdot 67}{3 \cdot 7 \cdot 11} = 0.5800865800865801$$