To identify the correct phrase that represents the algebraic expression [tex]\(\frac{1}{4} d + 7\)[/tex], let’s break down the components of the algebraic expression step-by-step:
1. Expression Breakdown:
- [tex]\(\frac{1}{4} d\)[/tex]: This part represents the product of one-fourth and the variable [tex]\(d\)[/tex] (which we can refer to as "a number").
- [tex]\(+ 7\)[/tex]: This indicates that we need to add 7 to the previously described product.
2. Analyzing Each Option:
- Option 1: "The product of one-fourth and a number, plus seven"
- This directly matches our expression:
- "The product of one-fourth" ([tex]\(\frac{1}{4}\)[/tex])
- "and a number" ([tex]\(d\)[/tex])
- "plus seven" (+7)
- This is a perfect match.
- Option 2: "The product of seven and a number"
- This would translate to [tex]\(7d\)[/tex]. This does not match the given expression as there is no one-fourth involved and the addition of 7 is missing.
- Option 3: "The product of one-fourth and seven, plus a number"
- This means [tex]\(\frac{1}{4} \times 7 + d\)[/tex], which simplifies to [tex]\(\frac{7}{4} + d\)[/tex]. This does not align with our given expression since the addition order and coefficients do not match.
- Option 4: "The product of seven and one-fourth"
- This translates to [tex]\(7 \times \frac{1}{4}\)[/tex], which simplifies to [tex]\(\frac{7}{4}\)[/tex]. There is no addition or variable involved, so this does not match either.
3. Conclusion:
- The phrase that accurately represents the algebraic expression [tex]\(\frac{1}{4}d + 7\)[/tex] is:
- "the product of one-fourth and a number, plus seven"
So, the correct option is indeed the first one.
