Factorials are the product of all positive integers from a given number down to 1. This document provides examples of calculating factorials such as 4! = 24 and discusses the rules for operations involving factorials such as cancellation rules that apply when dividing factorials. Practice problems are included with explanations to reinforce understanding of how to calculate and operate with factorial expressions.

1. Factorials A Quick and Easy Guide RAFS Education

2. Definition A facortial is the product of all positive numbers from n down. Written as: n!

3. Examples 10! = 10*9*8*7*6*5*4*3*2*1 5! = 5*4*3*2*1 1! = 1*1 0! = 1

4. Examples 3!+3! ≠ 6! Why? 3! = 3*2*1 = 6 3!+3! = 12 6! = 6*5*4*3*2*1 = 720 12 ≠ 720

5. Examples Take the following: The answer is: (19*18*17*16*15*14*13*12*11) This is because when dividing factorials, the rules for cancelling out that apply to fractions also apply to factorials.

6. Practice Example 1) Solve: 4! Example 2) Solve: 2!+3! Example 3) Solve: 5!/2! Example 4) Solve: 6!-4! (Are the following true?) Example 5) 4!+4! = 8! Example 6) 7!*6! = 10! Example 7) 5! = 5*4!

7. Answers and Explanations Ex1) 4! = 4*3*2*1 = 24 Ex2) 2!+3! = (2*1)+(3*2*1) = 2+6 = 8 Ex3) 5!/2! = = 5*4*3 = 60 Ex4) 6!-4! = (6*5*4*3*2*1)-(4*3*2*1) = 720-24 = 696 Ex5) No. 4!+4! ≠ 8! Because 48 ≠ 40,320

8. Answers and Explanations Cont'd Ex6) Yes. 7!*6! = 10! Because 720*5040 = 3628800 Ex7) Yes. 5! = 5*4! Because 5*(4*3*2*1) = 120 and 5! = 120

9. End Learn anything?