# Algebra II : Factorials

## Example Questions

### Example Question #51 : Factorials

Explanation:

Simplify the factorials in each fraction by canceling common factors in the numerator and denominator. It would be helpful to write this in expanded form but the factorials are too large for this to be feasible.

### Example Question #52 : Factorials

Explanation:

First, simplify the factorials in each fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form.

You can now turn this into a multiplication problem and flip the second fraction

### Example Question #53 : Factorials

Explanation:

First, simplify the factorials in each fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form.

It is easiest to combine these numbers into one fraction. The 5! will go into the numerator

### Example Question #54 : Factorials

Explanation:

Simplify the factorials in each fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form.

### Example Question #55 : Factorials

Explanation:

Simplify the factorials the fraction by canceling common factors in the numerator and denominator. Normally, it would help to write out the factorials in expanded form, but since these are larger factorials that is not feasible. The best approach to cancelling these is thinking that 20! will be completely gone by taking it out of 25! and 5! will be completely gone by taking it out of 10!

Then reduce this to lowest terms.

### Example Question #56 : Factorials

Explanation:

Simplify the factorials in each fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form.

Since it is division of fractions change the division sign to multiplication and flip the second fraction

### Example Question #57 : Factorials

Explanation:

Simplify the factorials in the fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form, but I would suggest cancelling out the 7! in the numerator and denominator first.

Then reduce the fraction to lowest terms

### Example Question #58 : Factorials

Explanation:

Simplify the factorials in the fraction by canceling common factors in the numerator and denominator. It can help to write it in expanded form.

Combine each of the fractions into one fraction.

### Example Question #59 : Factorials

Divide the factorials:

Explanation:

Dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

Write out the terms of the factorials.

Cancel all common terms.

### Example Question #60 : Factorials

Divide the factorials:

Explanation:

Evaluate the terms in parentheses first.  Do not distribute the integer through the parentheses or this will change the value of the factorial!

The common terms in the numerator and denominator can be simplified.