Solve 1/2,2+1/6,8+1/8,6

$$\frac { 1 } { 2,2 } + \frac { 1 } { 6,8 } + \frac { 1 } { 8,6 }$$

Evaluate

$$\frac{11545}{16082}\approx 0,717883348$$

Solution Steps

Expand \frac{1}{2,2} by multiplying both numerator and the denominator by 10.

$$\frac{10}{22}+\frac{1}{6,8}+\frac{1}{8,6}$$

Reduce the fraction \frac{10}{22} to lowest terms by extracting and canceling out 2.

$$\frac{5}{11}+\frac{1}{6,8}+\frac{1}{8,6}$$

Expand \frac{1}{6,8} by multiplying both numerator and the denominator by 10.

$$\frac{5}{11}+\frac{10}{68}+\frac{1}{8,6}$$

Reduce the fraction \frac{10}{68} to lowest terms by extracting and canceling out 2.

$$\frac{5}{11}+\frac{5}{34}+\frac{1}{8,6}$$

Least common multiple of 11 and 34 is 374. Convert \frac{5}{11} and \frac{5}{34} to fractions with denominator 374.

$$\frac{170}{374}+\frac{55}{374}+\frac{1}{8,6}$$

Since \frac{170}{374} and \frac{55}{374} have the same denominator, add them by adding their numerators.

$$\frac{170+55}{374}+\frac{1}{8,6}$$

Add 170 and 55 to get 225.

$$\frac{225}{374}+\frac{1}{8,6}$$

Expand \frac{1}{8,6} by multiplying both numerator and the denominator by 10.

$$\frac{225}{374}+\frac{10}{86}$$

Reduce the fraction \frac{10}{86} to lowest terms by extracting and canceling out 2.

$$\frac{225}{374}+\frac{5}{43}$$

Least common multiple of 374 and 43 is 16082. Convert \frac{225}{374} and \frac{5}{43} to fractions with denominator 16082.

$$\frac{9675}{16082}+\frac{1870}{16082}$$

Since \frac{9675}{16082} and \frac{1870}{16082} have the same denominator, add them by adding their numerators.

$$\frac{9675+1870}{16082}$$

Add 9675 and 1870 to get 11545.

$$\frac{11545}{16082}$$

Factor

$$\frac{5 \cdot 2309}{2 \cdot 11 \cdot 17 \cdot 43} = 0.7178833478423081$$