Math worksheet designed to teach students how to translate verbal phrases into algebraic expressions, including examples and key word guidance.

Let's solve this step-by-step based on the worksheet titled "Translating Verbal Phrases to Algebraic Expressions".

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🔍 Step 1: Fill in the KEY WORDS section

We are asked to identify key words that indicate operations and write the expressions accordingly.

| Phrase | Expression |
|-------|------------|
| The SUM of ________ and ________: | $ a + b $ |
| The DIFFERENCE of ________ and ________: | $ a - b $ |
| The PRODUCT of ________ and ________: | $ a \cdot b $ or $ ab $ |
| The QUOTIENT of ________ and ________: | $ \frac{a}{b} $ |

> ✔ So we fill in:
> - The SUM of [first number] and [second number]: $ a + b $
> - The DIFFERENCE of [first number] and [second number]: $ a - b $
> - The PRODUCT of [first number] and [second number]: $ a \cdot b $
> - The QUOTIENT of [first number] and [second number]: $ \frac{a}{b} $

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🧠 Important Notes:

- "Less than" means subtract the first number from the second, so order matters!
- Example: "5 less than x" → $ x - 5 $, not $ 5 - x $
- "More than" means add the first number to the second
- Example: "8 more than x" → $ x + 8 $

> 💡 Remember: Switch the order for "less than"!

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✏️ Now, let’s solve each problem:

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#### 1) the sum of 8 and t
- "Sum" → addition
- $ 8 + t $

✔ Answer: $ 8 + t $

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#### 2) the quotient of g and 15
- "Quotient" → division
- $ \frac{g}{15} $

✔ Answer: $ \frac{g}{15} $

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#### 3) the product of 5 and b
- "Product" → multiplication
- $ 5 \cdot b $ or $ 5b $

✔ Answer: $ 5b $

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#### 4) the difference of 32 and x
- "Difference" → subtraction
- "Of 32 and x" → $ 32 - x $

✔ Answer: $ 32 - x $

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#### 5) Eight more than x
- "More than" → addition
- Add 8 to x → $ x + 8 $

✔ Answer: $ x + 8 $

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#### 6) Six less than p
- "Less than" → subtract 6 from p (switch order!)
- $ p - 6 $

✔ Answer: $ p - 6 $

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#### 7) 14 less than f
- "Less than" → subtract 14 from f
- $ f - 14 $

✔ Answer: $ f - 14 $

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#### 8) p more than 10
- "More than" → add p to 10
- $ 10 + p $

✔ Answer: $ 10 + p $

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#### 9) 3 more runs than Pirates scored
- Let $ r $ = number of runs Pirates scored
- "3 more than" → $ r + 3 $

✔ Answer: $ r + 3 $

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#### 10) 12 less than some number
- Let $ n $ = some number
- "12 less than" → subtract 12 from $ n $
- $ n - 12 $

✔ Answer: $ n - 12 $

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✔ Final Answers:

1. $ 8 + t $
2. $ \frac{g}{15} $
3. $ 5b $
4. $ 32 - x $
5. $ x + 8 $
6. $ p - 6 $
7. $ f - 14 $
8. $ 10 + p $
9. $ r + 3 $
10. $ n - 12 $

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📌 Summary Tips:

- "Sum" → Addition (+)
- "Difference" → Subtraction (−), order matters!
- "Product" → Multiplication (× or ·)
- "Quotient" → Division (÷ or /)
- "Less than" → Reverse the order: e.g., “5 less than x” → $ x - 5 $
- "More than" → Add: e.g., “8 more than x” → $ x + 8 $

Let me know if you'd like this as a printable version or with visual examples!