Sure, let's break it down step-by-step. Translating words into algebraic expressions often involves identifying specific keywords that correspond to different mathematical operations. Let’s fill in the table with common phrases that indicate each operation:
1. Add:
- "Sum of"
- "Increased by"
- "More than"
- "Plus"
- "Added to"
- Example: "The sum of [tex]\(x\)[/tex] and 5" translates to [tex]\(x + 5\)[/tex].
2. Subtract:
- "Difference between"
- "Decreased by"
- "Less than"
- "Minus"
- "Subtracted from"
- Example: "The difference between [tex]\(x\)[/tex] and 5" translates to [tex]\(x - 5\)[/tex].
3. Multiply:
- "Product of"
- "Times"
- "Multiplied by"
- "Of"
- Example: "The product of [tex]\(x\)[/tex] and 5" translates to [tex]\(5x\)[/tex].
4. Divide:
- "Quotient of"
- "Divided by"
- "Per"
- "Ratio of"
- Example: "The quotient of [tex]\(x\)[/tex] and 5" translates to [tex]\(\frac{x}{5}\)[/tex].
Here's the filled-in table for clarity:
\begin{tabular}{|l|l|l|l|}
\hline
Add & Subtract & Multiply & Divide \\
\hline
Sum of & Difference between & Product of & Quotient of \\
Increased by & Decreased by & Times & Divided by \\
More than & Less than & Multiplied by & Per \\
Plus & Minus & Of & Ratio of \\
Added to & Subtracted from & & \\
\hline
\end{tabular}
Always remember to carefully read the context of the problem to correctly identify which operation is being described.
