To solve the problem of identifying which algebraic expression represents the phrase "four times a number," let's break down the phrase step-by-step:
1. Understanding the Components:
- "Four times" refers to multiplying by four.
- "A number" can be represented by a variable, often denoted as [tex]\(c\)[/tex] or any other letter.
2. Constructing the Expression:
- To express "four times a number," we need to multiply the variable [tex]\(c\)[/tex] by 4.
3. Formulating the Expression:
- The multiplication of the number [tex]\(c\)[/tex] by 4 is written as [tex]\(4c\)[/tex].
4. Option Comparison:
- [tex]\(4 + c\)[/tex]: This represents adding 4 to a number [tex]\(c\)[/tex], not multiplying.
- [tex]\(c - 4\)[/tex]: This represents subtracting 4 from a number [tex]\(c\)[/tex], not multiplying.
- [tex]\(4 \div c\)[/tex]: This represents dividing 4 by a number [tex]\(c\)[/tex], not multiplying.
- [tex]\(4c\)[/tex]: This represents four times a number [tex]\(c\)[/tex], which is exactly what we are looking for.
Therefore, the algebraic expression that represents the phrase "four times a number" is \[tex]$4c\$[/tex].
