OPERATIONS WITH FACTIRIALS WORKSHEET
Problem 1 :
3! + 2! =
Problem 2 :
3! + 6! =
Problem 3 :
(3!)2 =
Problem 4 :
5! + 4! =
Problem 5 :
4! - 5! + 4 =
Problem 6 :
2! × 5 - 12 =
Problem 7 :
(2! + 1!)3 =
Problem 8 :
(3! + 0!)3 =
Problem 9 :
(2! 0!)4 - 1 =
Problem 10 :
Problem 11 :
Problem 12 :
Problem 13 :
Problem 14 :
Problem 15 :
Problem 16 :
Problem 17 :
Problem 18 :
Problem 19 :
Answer Key
|
1) 8 2) 726 3) 36 4) 144 5) -92 6) -2 7) 27 8) 343 9) 15 10) 210 |
11) 504 12) 36 13) 6375600 14) 1463 15) 45 16) 970200 17) 1001 18) 40040 19) 2970 |
Write as a product using factorization:
Problem 1 :
5! + 4!
Problem 2 :
11! - 10!
Problem 3 :
6! + 8!
Problem 4 :
12! - 10!
Problem 5 :
9! + 8! + 7!
Problem 6 :
7! - 6! + 8!
Problem 7 :
12! - 2 ×11!
Problem 8 :
3 × 9! + 5 × 8!
Simplify using factorization :
Problem 1 :
(12! - 11!) / 11
Problem 2 :
(10! + 9!) / 11
Problem 3 :
(10! - 8!) / 89
Problem 4 :
(10! - 9!) / 9!
Problem 5 :
(6! + 5! - 4!) / 4!
Problem 6 :
(n! + (n - 1)!) / (n - 1)!
Problem 7 :
(n! - (n - 1)!) / n - 1
Problem 8 :
(n + 2)! + [(n + 1)! / (n + 3)]
Answer Key
|
1) 6 × 4! 2) 10 × 10! 3) 57 × 6! 4) 131 × 10! 5) 81 × 7! 6) 62 × 6! 7) 10 × 11! 8) 32 × 8! |
1) 11! 2) 9! 3) 8! 4) 9 5) 34 6) n + 1 7) (n - 1)! 8) (n + 1)! |
Simplify the following expressions.
Problem 1 :
(n + 2)! / n!
Problem 2 :
n / n!
Problem 3 :
(n - 1)! ∙ n! / (n!)²
Problem 4 :
(n + 5)! / (n + 1)!
Problem 5 :
((n + 1)!)³ / (n!)³
Problem 6 :
(n² - 1)! / (n²)!
Problem 7 :
(2n)! / (2n - 2)! ∙ 2!
Problem 8 :
(n - 1)! (n2 + n)
Problem 9 :
(n + 5) (n + 4) (n + 3)!
Problem 10 :
n! (n2 + 3n + 2)
Answer Key
1) (n + 2) (n + 1)
2) 1 / (n - 1)!
3) 1/n
4) (n + 5) (n + 4) (n + 3) (n + 2)
5) (n + 1)3
6) 1/n²
7) n (2n - 1)
8) (n - 1)! n(n + 1) = (n + 1)!
9) (n + 5) (n + 4) (n + 3)! = (n + 5)!
10) (n + 2)!
Simplify without using a calculator.
Problem 1 :
6! / 5!
Problem 2 :
6! / 4!
Problem 3 :
6! / 7!
Problem 4 :
4! / 6!
Problem 5 :
100! / 99!
Problem 6 :
7! / (5! × 2!)
Simplify:
Problem 7 :
n! / (n - 1)!
Problem 8 :
(n + 2)! / n!
Problem 9 :
(n + 1)! / (n - 1)!
Simplify the following expressions.
Problem 10 :
5! / 6!
Problem 11 :
7! / 5!
Problem 12 :
(3!)² / 9
Problem 13 :
(3! ∙ 4!) / 5!
Problem 14 :
9! /(5! ∙ 3!)
Problem 15 :
(4 - 1)! / 4!
Problem 16 :
(2 ∙ 3)! / 3!
Problem 17 :
88! / 90!
Problem 18 :
(77! ∙ 2!)/ 78!
Problem 19 :
38! ∙ 3! / 39!
Answer Key
|
1) 6 2) 30 3) 1/7 4) 1/30 5) 100 6) 21 7) n 8) (n + 2) (n + 1) 9) n(n + 1) 10) 1/6 |
11) 42 12) 4 13) 6/5 14) 504 15) 1/4 16) 120 17) 1/8010 18) 1/39 19) 2/13 |
Express in factorial form:
Problem 1 :
7 × 6 × 5
Problem 2 :
10 × 9
Problem 3 :
11 × 10 × 9 × 8 × 7
Problem 4 :
(13 × 12 × 11) / (3 × 2 × 1)
Problem 5 :
1 / (6 × 5 × 4)
Problem 6 :
(4 × 3 × 2 × 1) / (20 × 19 × 18 × 17)
Problem 7 :
1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ 6 ∙ 7 ∙ 8
Problem 8 :
1 ∙ 2 ∙ 3……100
Problem 9 :
1 ∙ 2 ∙ 3 ∙ 4 …. (n - 2) ∙ (n - 1) ∙ n
Problem 10 :
1 ∙ 2 ∙ 3 ∙ …. 56 ∙ 57 ∙ 58
Problem 11 :
1 ∙ 2 ∙ 3 ∙ 4 ∙ 5 ∙ … (5n - 4) ∙ (5n - 3) ∙ (5n - 2) ∙ (5n - 1)
Answer Key
|
1) 7! / 4! 2) 10! / 8! 3) 11! / 6! 4) 13! / (10! × 3!) 5) 3! / 6! 6) (4! 16!) / 20! |
7) 8! 8) 100! 9) n! 10) 58! 11) (5n - 1)! |
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