*This Math quiz is called 'Calculations - Factorials - Introduction' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

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Ah yes, here we are being hit with yet another new math vocabulary word - **factorials**. You’ll probably be very happy to learn that factorials are really very easy and even fun. Later on as you progress in your math classes such as in trigonometry or calculus, or even physics, you will learn how to use factorials in several different formulas. However, for this quiz, we are just going to get comfortable with understanding the very basics of factorials.

Okay, so what is a factorial? **A factorial is the sum of all whole numbers multiplied in ascending order that precede the factorial number until the factorial number is reached.** So what does that mean? Well, let’s look at a factorial number. The factorial number is **6! **

Did you see what was highlighted? **6!** The exclamation point is part of the number. So if you see the number “6” standing alone it is just the number 6 but if you see it written as “**6!**” then you have the factorial 6!

Now, we learned that the factorial is the sum of all the whole numbers multiplied in ascending order that precede the factorial number. What this now means is that you find all of the whole numbers that precede (come before) the factorial number 6! These include the numbers, 1, 2, 3, 4 and 5. Next we are told that we include the numbers until the factorial number is reached. This means we have 1, 2, 3, 4, 5 and 6.

Next we are told that the factorial is the sum of the whole numbers multiplied in ascending order. This means we need to multiply each number as we ascend to the factorial number so it will look like the following:

1 x 2 x 3 x 4 x 5 x 6

So we then work to find the sum.

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = ** 720** (We stop here as we have reached the factorial number.)

720 is the sum of factorial 6! This math problem would then be written out in the following manner.

**6! = 720**

It can also be written as the factorial of **6!** is **720**.

See, it really is pretty easy isn’t it? Well then, if you think you feel ready, then see if you can find what the factorials are equal to in the next ten problems.

1.

7! = ?

4,050

4,250

5,040

5,080

2.

4! + 9! = ?

5,660,910

362,904

362,928

566,091

Working the problem we have

1 x 2 x 3 x 4

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

- and then -

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

__Solution__: 4! + 9! = 24 + 362,880 = 362,904

4! + 9! = 362,904

Answer (b) is the correct answer

1 x 2 x 3 x 4

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

- and then -

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

4! + 9! = 362,904

Answer (b) is the correct answer

3.

3! = ?

8

4

12

6

Working the problem we have

1 x 2 x 3

1 x 2 = 2

2 x 3 = 6

__Solution__: 3! = 6

Answer (d) is the correct answer

1 x 2 x 3

1 x 2 = 2

2 x 3 = 6

Answer (d) is the correct answer

4.

8! ÷ 4! x 2! = ?

3,160

3,260

3,360

3,460

Working the problem we have

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

- and then -

1 x 2 x 3 x 4

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

- and then

1 x 2 = 2

__Solution__: 8! ÷ 4! x 2!= 40,320 ÷ 24 = 1,680 x 2 = 3,360

8! ÷ 4! x 2!= 3,360

Answer (c) is the correct answer

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

- and then -

1 x 2 x 3 x 4

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

- and then

1 x 2 = 2

8! ÷ 4! x 2!= 3,360

Answer (c) is the correct answer

5.

11! ÷ 5! = ?

332,640

332,620

332,600

332,580

Working the problem we have

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

362,880 x 10 = 3,628,800

3,628,800 x 11 = 39,916,800

- and then -

1 x 2 x 3 x 4 x 5

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

__Solution__: 11! ÷ 5! = 39,916,800 ÷ 120 = 332,640

11! ÷ 5! = 332,640

Answer (a) is the correct answer

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

362,880 x 10 = 3,628,800

3,628,800 x 11 = 39,916,800

- and then -

1 x 2 x 3 x 4 x 5

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

11! ÷ 5! = 332,640

Answer (a) is the correct answer

6.

5! = ?

120

125

130

135

Working the problem we have

1 x 2 x 3 x 4 x 5

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

__Solution__: 5! = 120

Answer (a) is the correct answer

1 x 2 x 3 x 4 x 5

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

Answer (a) is the correct answer

7.

10! = ?

3,428,800

342,880

3,628,800

362,880

Working the problem we have

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

362,880 x 10 = 3,628,800

__Solution__: 10! = 3,628,800

Answer (c) is the correct answer

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

40,320 x 9 = 362,880

362,880 x 10 = 3,628,800

Answer (c) is the correct answer

8.

7! - 6! = ?

3,420

4,320

2,430

4,540

Working the problem we have

1 x 2 x 3 x 4 x 5 x 6 x 7

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

- and then -

1 x 2 x 3 x 4 x 5 x 6

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

__Solution__: 7! - 6! = 5,040 - 720 = 4,320

7! - 6! = 4,320

Answer (b) is the correct answer

1 x 2 x 3 x 4 x 5 x 6 x 7

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

- and then -

1 x 2 x 3 x 4 x 5 x 6

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

7! - 6! = 4,320

Answer (b) is the correct answer

9.

6! x 2! = ?

1,442

722

732

1,440

Working the problem we have

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

- and then -

1 x 2

1 x 2 = 2

__Solution__: 6! x 2! = 720 x 2 = 1,440

6! x 2! = 1,440

Answer (d) is the correct answer

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

- and then -

1 x 2

1 x 2 = 2

6! x 2! = 1,440

Answer (d) is the correct answer

10.

8! = ?

35,320

40,320

40,040

404,020

Working the problem we have

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

__Solution__: 8! = 40,320

Answer (b) is the correct answer

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

5,040 x 8 = 40,320

Answer (b) is the correct answer

The next step is:

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1 x 2 x 3 x 4 x 5 x 6 x 7

1 x 2 = 2

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

120 x 6 = 720

720 x 7 = 5,040

7! = 5,040Solution:Answer (c) is the correct answer