Solve 1/10!/frac{1{8!}-1/9!}

$$\frac { \frac { 1 } { 10 ! } } { \frac { 1 } { 8 ! } - \frac { 1 } { 9 ! } }$$

Evaluate

$$\frac{1}{80}=0.0125$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{\frac{1}{3628800}}{\frac{1}{8!}-\frac{1}{9!}}$$

The factorial of 8 is 40320.

$$\frac{\frac{1}{3628800}}{\frac{1}{40320}-\frac{1}{9!}}$$

The factorial of 9 is 362880.

$$\frac{\frac{1}{3628800}}{\frac{1}{40320}-\frac{1}{362880}}$$

Least common multiple of 40320 and 362880 is 362880. Convert \frac{1}{40320} and \frac{1}{362880} to fractions with denominator 362880.

$$\frac{\frac{1}{3628800}}{\frac{9}{362880}-\frac{1}{362880}}$$

Since \frac{9}{362880} and \frac{1}{362880} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{3628800}}{\frac{9-1}{362880}}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{1}{3628800}}{\frac{8}{362880}}$$

Reduce the fraction \frac{8}{362880} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{1}{3628800}}{\frac{1}{45360}}$$

Divide \frac{1}{3628800} by \frac{1}{45360} by multiplying \frac{1}{3628800} by the reciprocal of \frac{1}{45360}.

$$\frac{1}{3628800}\times 45360$$

Multiply \frac{1}{3628800} and 45360 to get \frac{45360}{3628800}.

$$\frac{45360}{3628800}$$

Reduce the fraction \frac{45360}{3628800} to lowest terms by extracting and canceling out 45360.

$$\frac{1}{80}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 5} = 0.0125$$