Solve =(1/40+1/62+1/56+1/60)*frac{1}{3}

$$= ( \frac { 1 } { 40 } + \frac { 1 } { 62 } + \frac { 1 } { 56 } + \frac { 1 } { 60 } ) \times \frac { 1 } { 3 }$$

Evaluate

$$\frac{197}{7812}\approx 0.025217614$$

Solution Steps

Least common multiple of 40 and 62 is 1240. Convert \frac{1}{40} and \frac{1}{62} to fractions with denominator 1240.

$$\left(\frac{31}{1240}+\frac{20}{1240}+\frac{1}{56}+\frac{1}{60}\right)\times \frac{1}{3}$$

Since \frac{31}{1240} and \frac{20}{1240} have the same denominator, add them by adding their numerators.

$$\left(\frac{31+20}{1240}+\frac{1}{56}+\frac{1}{60}\right)\times \frac{1}{3}$$

Add 31 and 20 to get 51.

$$\left(\frac{51}{1240}+\frac{1}{56}+\frac{1}{60}\right)\times \frac{1}{3}$$

Least common multiple of 1240 and 56 is 8680. Convert \frac{51}{1240} and \frac{1}{56} to fractions with denominator 8680.

$$\left(\frac{357}{8680}+\frac{155}{8680}+\frac{1}{60}\right)\times \frac{1}{3}$$

Since \frac{357}{8680} and \frac{155}{8680} have the same denominator, add them by adding their numerators.

$$\left(\frac{357+155}{8680}+\frac{1}{60}\right)\times \frac{1}{3}$$

Add 357 and 155 to get 512.

$$\left(\frac{512}{8680}+\frac{1}{60}\right)\times \frac{1}{3}$$

Reduce the fraction \frac{512}{8680} to lowest terms by extracting and canceling out 8.

$$\left(\frac{64}{1085}+\frac{1}{60}\right)\times \frac{1}{3}$$

Least common multiple of 1085 and 60 is 13020. Convert \frac{64}{1085} and \frac{1}{60} to fractions with denominator 13020.

$$\left(\frac{768}{13020}+\frac{217}{13020}\right)\times \frac{1}{3}$$

Since \frac{768}{13020} and \frac{217}{13020} have the same denominator, add them by adding their numerators.

$$\frac{768+217}{13020}\times \frac{1}{3}$$

Add 768 and 217 to get 985.

$$\frac{985}{13020}\times \frac{1}{3}$$

Reduce the fraction \frac{985}{13020} to lowest terms by extracting and canceling out 5.

$$\frac{197}{2604}\times \frac{1}{3}$$

Multiply \frac{197}{2604} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{197\times 1}{2604\times 3}$$

Do the multiplications in the fraction \frac{197\times 1}{2604\times 3}.

$$\frac{197}{7812}$$

Factor

$$\frac{197}{2 ^ {2} \cdot 3 ^ {2} \cdot 7 \cdot 31} = 0.025217613927291348$$