Solve 1/120+1/20+1/100+1/130=

$$\frac { 1 } { 120 } + \frac { 1 } { 20 } + \frac { 1 } { 100 } + \frac { 1 } { 130 } =$$

Evaluate

$$\frac{593}{7800}\approx 0.076025641$$

Solution Steps

Least common multiple of 120 and 20 is 120. Convert \frac{1}{120} and \frac{1}{20} to fractions with denominator 120.

$$\frac{1}{120}+\frac{6}{120}+\frac{1}{100}+\frac{1}{130}$$

Since \frac{1}{120} and \frac{6}{120} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{120}+\frac{1}{100}+\frac{1}{130}$$

Add 1 and 6 to get 7.

$$\frac{7}{120}+\frac{1}{100}+\frac{1}{130}$$

Least common multiple of 120 and 100 is 600. Convert \frac{7}{120} and \frac{1}{100} to fractions with denominator 600.

$$\frac{35}{600}+\frac{6}{600}+\frac{1}{130}$$

Since \frac{35}{600} and \frac{6}{600} have the same denominator, add them by adding their numerators.

$$\frac{35+6}{600}+\frac{1}{130}$$

Add 35 and 6 to get 41.

$$\frac{41}{600}+\frac{1}{130}$$

Least common multiple of 600 and 130 is 7800. Convert \frac{41}{600} and \frac{1}{130} to fractions with denominator 7800.

$$\frac{533}{7800}+\frac{60}{7800}$$

Since \frac{533}{7800} and \frac{60}{7800} have the same denominator, add them by adding their numerators.

$$\frac{533+60}{7800}$$

Add 533 and 60 to get 593.

$$\frac{593}{7800}$$

Factor

$$\frac{593}{2 ^ {3} \cdot 3 \cdot 5 ^ {2} \cdot 13} = 0.07602564102564102$$