Let's break down the phrase "four times a number" step by step to form the correct algebraic expression:
1. Understand the Phrase:
The phrase "four times a number" indicates multiplication. We need to multiply the number by four.
2. Represent the Unknown Number:
Let’s represent the unknown number with a variable. Commonly, we use letters such as [tex]\( c \)[/tex] to denote this variable.
3. Form the Algebraic Expression:
- "Four" translates to the number [tex]\( 4 \)[/tex].
- "Times" means multiplication.
- "A number" is represented by the variable [tex]\( c \)[/tex].
4. Combine These Elements:
To express "four times a number", we combine [tex]\( 4 \)[/tex] and [tex]\( c \)[/tex] using multiplication. Multiplying [tex]\( 4 \)[/tex] by [tex]\( c \)[/tex] gives [tex]\( 4c \)[/tex].
Therefore, the algebraic expression that represents the phrase "four times a number" is [tex]\( 4c \)[/tex].
Let's eliminate the incorrect choices to affirm our understanding:
- [tex]\( 4 + c \)[/tex] implies adding [tex]\( 4 \)[/tex] to the unknown number, which is not what the phrase describes.
- [tex]\( c. 4 \)[/tex] is not a standard mathematical notation for multiplication.
- [tex]\( 4 + c \)[/tex] (repeated) again implies addition rather than multiplication.
Hence, the correct answer is:
[tex]\[ 4c \][/tex]
