To decipher the correct phrase for the algebraic expression \(\frac{1}{4} d + 7\), let's break it down step-by-step.
1. The term \(\frac{1}{4} d\) can be understood as the product of one-fourth and a number \(d\).
2. The term \(+ 7\) simply means adding seven to the previous product.
Let's analyze each phrase provided:
- The product of one-fourth and a number, plus seven:
This correctly describes \(\frac{1}{4} d + 7\), where we first multiply a number (represented by \(d\)) by one-fourth, and then add seven.
- The product of seven and a number:
This would be written as \(7d\), which does not match \(\frac{1}{4} d + 7\).
- The product of one-fourth and seven, plus a number:
This would translate to \(\frac{1}{4} \cdot 7 + d\), which is different from \(\frac{1}{4} d + 7\).
- The product of seven and one-fourth:
This would be written as \(7 \cdot \frac{1}{4}\), which equals \(\frac{7}{4}\) and does not involve a variable or match \(\frac{1}{4} d + 7\).
Therefore, the phrase that represents the algebraic expression \(\frac{1}{4} d + 7\) is:
The product of one-fourth and a number, plus seven.
