Solve (1/2+1/4+1/6+1/8+frac{1}{10})

$$( \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 6 } + \frac { 1 } { 8 } + \frac { 1 } { 10 } )$$

Evaluate

$$\frac{137}{120}\approx 1.141666667$$

Solution Steps

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

$$\frac{2}{4}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{9}{12}+\frac{2}{12}+\frac{1}{8}+\frac{1}{10}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{12}+\frac{1}{8}+\frac{1}{10}$$

Add 9 and 2 to get 11.

$$\frac{11}{12}+\frac{1}{8}+\frac{1}{10}$$

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{1}{8} to fractions with denominator 24.

$$\frac{22}{24}+\frac{3}{24}+\frac{1}{10}$$

Since \frac{22}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{24}+\frac{1}{10}$$

Add 22 and 3 to get 25.

$$\frac{25}{24}+\frac{1}{10}$$

Least common multiple of 24 and 10 is 120. Convert \frac{25}{24} and \frac{1}{10} to fractions with denominator 120.

$$\frac{125}{120}+\frac{12}{120}$$

Since \frac{125}{120} and \frac{12}{120} have the same denominator, add them by adding their numerators.

$$\frac{125+12}{120}$$

Add 125 and 12 to get 137.

$$\frac{137}{120}$$

Factor

$$\frac{137}{2 ^ {3} \cdot 3 \cdot 5} = 1\frac{17}{120} = 1.1416666666666666$$