Solve 3!/4!+4!/5!

$$\frac { 3 ! } { 4 ! } + \frac { 4 ! } { 5 ! }$$

Evaluate

$$\frac{9}{20}=0.45$$

Solution Steps

The factorial of 3 is 6.

$$\frac{6}{4!}+\frac{4!}{5!}$$

The factorial of 4 is 24.

$$\frac{6}{24}+\frac{4!}{5!}$$

Reduce the fraction \frac{6}{24} to lowest terms by extracting and canceling out 6.

$$\frac{1}{4}+\frac{4!}{5!}$$

The factorial of 4 is 24.

$$\frac{1}{4}+\frac{24}{5!}$$

The factorial of 5 is 120.

$$\frac{1}{4}+\frac{24}{120}$$

Reduce the fraction \frac{24}{120} to lowest terms by extracting and canceling out 24.

$$\frac{1}{4}+\frac{1}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{5}{20}+\frac{4}{20}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{20}$$

Add 5 and 4 to get 9.

$$\frac{9}{20}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 5} = 0.45$$