Solve 1/10+1/20+1/30+1/40

$$\frac { 1 } { 10 } + \frac { 1 } { 20 } + \frac { 1 } { 30 } + \frac { 1 } { 40 }$$

Evaluate

$$\frac{5}{24}\approx 0.208333333$$

Solution Steps

Least common multiple of 10 and 20 is 20. Convert \frac{1}{10} and \frac{1}{20} to fractions with denominator 20.

$$\frac{2}{20}+\frac{1}{20}+\frac{1}{30}+\frac{1}{40}$$

Since \frac{2}{20} and \frac{1}{20} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{20}+\frac{1}{30}+\frac{1}{40}$$

Add 2 and 1 to get 3.

$$\frac{3}{20}+\frac{1}{30}+\frac{1}{40}$$

Least common multiple of 20 and 30 is 60. Convert \frac{3}{20} and \frac{1}{30} to fractions with denominator 60.

$$\frac{9}{60}+\frac{2}{60}+\frac{1}{40}$$

Since \frac{9}{60} and \frac{2}{60} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{60}+\frac{1}{40}$$

Add 9 and 2 to get 11.

$$\frac{11}{60}+\frac{1}{40}$$

Least common multiple of 60 and 40 is 120. Convert \frac{11}{60} and \frac{1}{40} to fractions with denominator 120.

$$\frac{22}{120}+\frac{3}{120}$$

Since \frac{22}{120} and \frac{3}{120} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{120}$$

Add 22 and 3 to get 25.

$$\frac{25}{120}$$

Reduce the fraction \frac{25}{120} to lowest terms by extracting and canceling out 5.

$$\frac{5}{24}$$

Factor

$$\frac{5}{2 ^ {3} \cdot 3} = 0.20833333333333334$$