Solve 1/1.2+1/1.4+1/1.6+1/1.8

$$\frac{ 1 }{ 1.2 } + \frac{ 1 }{ 1.4 } + \frac{ 1 }{ 1.6 } + \frac{ 1 }{ 1.8 }$$

Evaluate

$$\frac{1375}{504}\approx 2.728174603$$

Solution Steps

Expand \frac{1}{1.2} by multiplying both numerator and the denominator by 10.

$$\frac{10}{12}+\frac{1}{1.4}+\frac{1}{1.6}+\frac{1}{1.8}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}+\frac{1}{1.4}+\frac{1}{1.6}+\frac{1}{1.8}$$

Expand \frac{1}{1.4} by multiplying both numerator and the denominator by 10.

$$\frac{5}{6}+\frac{10}{14}+\frac{1}{1.6}+\frac{1}{1.8}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}+\frac{5}{7}+\frac{1}{1.6}+\frac{1}{1.8}$$

Least common multiple of 6 and 7 is 42. Convert \frac{5}{6} and \frac{5}{7} to fractions with denominator 42.

$$\frac{35}{42}+\frac{30}{42}+\frac{1}{1.6}+\frac{1}{1.8}$$

Since \frac{35}{42} and \frac{30}{42} have the same denominator, add them by adding their numerators.

$$\frac{35+30}{42}+\frac{1}{1.6}+\frac{1}{1.8}$$

Add 35 and 30 to get 65.

$$\frac{65}{42}+\frac{1}{1.6}+\frac{1}{1.8}$$

Expand \frac{1}{1.6} by multiplying both numerator and the denominator by 10.

$$\frac{65}{42}+\frac{10}{16}+\frac{1}{1.8}$$

Reduce the fraction \frac{10}{16} to lowest terms by extracting and canceling out 2.

$$\frac{65}{42}+\frac{5}{8}+\frac{1}{1.8}$$

Least common multiple of 42 and 8 is 168. Convert \frac{65}{42} and \frac{5}{8} to fractions with denominator 168.

$$\frac{260}{168}+\frac{105}{168}+\frac{1}{1.8}$$

Since \frac{260}{168} and \frac{105}{168} have the same denominator, add them by adding their numerators.

$$\frac{260+105}{168}+\frac{1}{1.8}$$

Add 260 and 105 to get 365.

$$\frac{365}{168}+\frac{1}{1.8}$$

Expand \frac{1}{1.8} by multiplying both numerator and the denominator by 10.

$$\frac{365}{168}+\frac{10}{18}$$

Reduce the fraction \frac{10}{18} to lowest terms by extracting and canceling out 2.

$$\frac{365}{168}+\frac{5}{9}$$

Least common multiple of 168 and 9 is 504. Convert \frac{365}{168} and \frac{5}{9} to fractions with denominator 504.

$$\frac{1095}{504}+\frac{280}{504}$$

Since \frac{1095}{504} and \frac{280}{504} have the same denominator, add them by adding their numerators.

$$\frac{1095+280}{504}$$

Add 1095 and 280 to get 1375.

$$\frac{1375}{504}$$

Factor

$$\frac{11 \cdot 5 ^ {3}}{7 \cdot 2 ^ {3} \cdot 3 ^ {2}} = 2\frac{367}{504} = 2.7281746031746033$$