The given expression is:
[tex]\[ r + r + r + r + r \][/tex]
To find an equivalent expression, we can look at the terms being added together. Each term is [tex]\( r \)[/tex], and there are five such terms. When you add the same term multiple times, it is equivalent to multiplying the term by the number of times it appears. Hence, we can rewrite the sum as a product:
[tex]\[ r + r + r + r + r = 5r \][/tex]
Let's confirm the possibilities provided:
1. [tex]\( 5r \)[/tex]: This expression indicates that [tex]\( r \)[/tex] is multiplied by 5, which is exactly what we have determined.
2. [tex]\( \frac{r}{5} \)[/tex]: This implies dividing [tex]\( r \)[/tex] by 5, which is not equivalent to the repeated addition of [tex]\( r \)[/tex].
3. 5: This is just the number 5, without any variable involved, thus not representing the repeated addition of [tex]\( r \)[/tex].
4. [tex]\( r^5 \)[/tex]: This implies raising [tex]\( r \)[/tex] to the power of 5, which is also not equivalent to the repeated addition of [tex]\( r \)[/tex].
Therefore, the expression equivalent to [tex]\( r + r + r + r + r \)[/tex] is:
[tex]\[ 5r \][/tex]
