Solve 1/10!-30+1/615

$$\frac { 1 } { 10 ! - 30 } + \frac { 1 } { 615 }$$

Evaluate

$$\frac{80653}{49593190}\approx 0.001626292$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{1}{3628800-30}+\frac{1}{615}$$

Subtract 30 from 3628800 to get 3628770.

$$\frac{1}{3628770}+\frac{1}{615}$$

Least common multiple of 3628770 and 615 is 148779570. Convert \frac{1}{3628770} and \frac{1}{615} to fractions with denominator 148779570.

$$\frac{41}{148779570}+\frac{241918}{148779570}$$

Since \frac{41}{148779570} and \frac{241918}{148779570} have the same denominator, add them by adding their numerators.

$$\frac{41+241918}{148779570}$$

Add 41 and 241918 to get 241959.

$$\frac{241959}{148779570}$$

Reduce the fraction \frac{241959}{148779570} to lowest terms by extracting and canceling out 3.

$$\frac{80653}{49593190}$$

Factor

$$\frac{59 \cdot 1367}{2 \cdot 5 \cdot 29 \cdot 41 \cdot 43 \cdot 97} = 0.001626291835633078$$