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Chapter 12: Problem 9

Evaluate each expression. $$ 4 ! \cdot 5 $$

Short Answer

Expert verified
120

Step by step solution

01

Understand the Factorial

The factorial of a number, denoted by the symbol '!', means to multiply all whole numbers from that number down to 1. For example, the factorial of 4, written as 4!, is calculated as 4 脳 3 脳 2 脳 1.
02

Calculate 4!

To find the value of 4!, multiply 4 脳 3 脳 2 脳 1.So, 4! = 4 脳 3 脳 2 脳 1 = 24.
03

Multiply by 5

Now take the result from Step 2 (which is 24) and multiply it by 5.So, 24 脳 5 = 120.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factorial
A factorial of a number is a way to multiply a series of descending natural numbers. It's represented by the exclamation mark '!' after a number. For example, 4! means 4 times 3 times 2 times 1. This gives 4 脳 3 脳 2 脳 1, which is 24. Factorials are handy in many areas like algebra, combinatorics, and calculus. They help in calculating permutations and combinations. When learning factorials, remember that factorial of zero (0!) is 1. It's a special rule.
Step-by-Step Solutions
Breaking down problems into smaller steps can make difficult tasks easier. Let's look at the given problem: 4! 脳 5. First, we solve 4! by multiplying 4 脳 3 脳 2 脳 1 to get 24. The next step is to multiply this result by 5, so 24 脳 5 gives 120. This step-by-step method ensures you don't miss any stages and helps you understand the process more clearly. Keep practicing with different numbers. It'll help you become confident in solving factorial problems.
Multiplication
Multiplication is one of the basic arithmetic operations. It's repeated addition. For example, 4 脳 3 means adding 4 three times: 4 + 4 + 4. It's faster and simpler than adding numbers repeatedly. Multiplication is crucial in evaluating factorials like 4! 脳 5. To multiply two numbers: write down the numbers, multiply the digits, and add up results properly. With practice, multiplication can become second nature. It's a key skill in math, useful in many real-life scenarios like calculating area, budgeting, and more.

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Most popular questions from this chapter

Evaluate each expression. $$ 4 ! $$

Evaluate the indicated term for each geometric sequence. $$ a_{1}=1, r=3 ; a_{15} $$

Find a general term \(a_{n}\) for the given terms of each sequence. $$ \frac{2}{5}, \frac{3}{6}, \frac{4}{7}, \frac{5}{8}, \ldots $$

If the given sequence is geometric, find the common ratio \(r\) If the sequence is not geometric, say so. See Example 1 . $$ \frac{2}{3},-\frac{2}{15}, \frac{2}{75},-\frac{2}{375}, \dots $$

If the given sequence is geometric, find the common ratio \(r\) If the sequence is not geometric, say so. See Example 1 . $$ 1,-3,9,-27,81, \ldots $$
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