An Enrichment Lesson for Math 10 (Factorials)

Factorials

Welcome to our Math Lesson!

Our lesson is all about Factorials.

I hope you can still remember your Lesson from our first Learning Activity Sheet (LAS). What are Factorials? Do you have an idea?

Okay. a Factorial is...

• the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. ... Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. 

• Factorial zero is defined as equal to 1.

Examples of factorials

• On the right you can see some factorials.

• What do you think is the answer to 7! or 7 factorial?

Multiple Choice

7! = ?

• 1x2x3x4x5x6x7 = 5040

• 1x2x3x4x5x6=2520

• 7x7=49

• 7x7x7x7x7x7x7=823543

Multiple Choice

That's easy. how about 4! or 4x3x2x1?

• 24

• 12

• 64

• 4

Multiple Select

I know that's easy. How about 3! + 4!

• 6 + 24 = 30

• 3 + 4 = 7

• 6 + 12 = 18

That was fast. I know you can do it. Anyway, as in the last example, we can actually use operations in factorials.

Let's see some more examples...

See the example on the right. Take a closer look. The process is division. It is a long process.

• Of course, there is a short cut to that...

• Wanna see? Just click next when you're ready.

Here's the shorter version. You can actually "cancel" both 7! much like any number you divide.

Factorials can be treated as "factors". That is why you can cancel those similar values on the numerator and the denominator.

Let's have a quick test.

Are you ready? Click next.

Multiple Select

5!

• 20

• 120

• 60

Multiple Select

0!

• 1

• 0

• 2

Multiple Select

2! + 3!

• 5

• 6

• 8

Multiple Select

4! - 2!

• 20

• 22

• 24

• 2

Multiple Select

3! x 3!

• 30

• 9

• 36

Multiple Select

 $\frac{7!}{5!}$  

• 7

• 42

• 35

How did you get the right answer on the last example?

7! / 5! is actually 7x6x5! divided by 5! so you can cancel 5! and what is left is 7x6 = 42. Easy.

Thanks for taking our Enrichment lesson for Math 10.

See you next time!