To determine which phrase represents the algebraic expression [tex]\(\frac{1}{4} \alpha + 7\)[/tex], let's carefully analyze each part of the expression and match it with the given choices.
1. Algebraic Expression Breakdown:
- [tex]\(\frac{1}{4} \alpha\)[/tex]: This part represents the product of one-fourth (which is [tex]\(\frac{1}{4}\)[/tex]) and a number (represented by [tex]\(\alpha\)[/tex]).
- [tex]\(+ 7\)[/tex]: This part indicates that after computing the product of one-fourth and the number, we add 7 to the result.
2. Matching to Choices:
- The product of one-fourth and a number, plus seven: This phrase exactly matches our breakdown. It indicates multiplying a number by one-fourth and then adding seven. This corresponds to the expression [tex]\(\frac{1}{4} \alpha + 7\)[/tex].
- The product of seven and a number: This phrase would correspond to [tex]\(7 \alpha\)[/tex], which is not what we have in our expression.
- The product of one-fourth and seven, plus a number: This phrase would correspond to [tex]\(\frac{1}{4} \times 7 + \alpha\)[/tex] or [tex]\(\frac{7}{4} + \alpha\)[/tex], which again is not what we see in our expression.
- The product of seven and one-fourth: This phrase represents [tex]\(\frac{7}{4}\)[/tex], which does not include any variable and, therefore, does not match our expression.
Given the detailed breakdown and evaluation, the correct phrase that represents the algebraic expression [tex]\(\frac{1}{4} \alpha + 7\)[/tex] is:
The product of one-fourth and a number, plus seven
Thus, the correct choice is the first one.
