This worksheet helps students learn the key vocabulary needed to turn word problems into math equations.

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

---

🔍 Step 1: Fill in the blanks at the top

> To translate statements into expressions and equations:
> - Identify key words that indicate the operation.
> - Write the numbers/variables in the correct order.

✔ So, the first blank should be:
Key words

---

🧩 Fill in the KEY WORDS section

We need to match the phrases with their algebraic forms:

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

So fill in:

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

> 💡 Note: "Difference" means subtraction, and order matters — it's *first minus second* unless specified otherwise.

---

✔ Now solve each problem

#### 1) the sum of 8 and t
→ Addition: $ 8 + t $

#### 2) the quotient of g and 15
→ Division: $ \frac{g}{15} $

#### 3) the product of 5 and b
→ Multiplication: $ 5b $ (or $ 5 \cdot b $)

#### 4) the difference of 32 and x
→ Subtraction: $ 32 - x $

---

⚠️ Important Tip: "Less than" and "More than"

> "LESS THAN" → reverse the order!
> Example: “5 less than Jennifer earned” = $ d - 5 $, not $ 5 - d $

> "MORE THAN" → add in order

---

#### 5) Eight more than x
→ "more than" means addition: $ x + 8 $

> ✘ Not $ 8 + x $? Wait — actually, yes, but "eight more than x" means you start with $ x $ and add 8 → $ x + 8 $.
> ✔ Correct: $ x + 8 $

#### 6) Six less than p
→ "less than" → reverse order: $ p - 6 $

#### 7) 14 less than f
→ $ f - 14 $

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

> 💡 Even though "p more than 10" might sound like $ p + 10 $, both are equivalent. But standard form is $ 10 + p $, since we're adding to 10.

But note: "p more than 10" means $ 10 + p $

✔ So: $ 10 + p $

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

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

---

✔ 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 $ (where $ r $ = runs Pirates scored)
10) $ n - 12 $ (where $ n $ = some number)

---

📝 Summary Tips:

| Phrase | Operation | Order |
|--------|-----------|-------|
| Sum of A and B | Addition | $ A + B $ |
| Difference of A and B | Subtraction | $ A - B $ |
| Product of A and B | Multiplication | $ A \cdot B $ or $ AB $ |
| Quotient of A and B | Division | $ \frac{A}{B} $ |
| A more than B | Addition | $ B + A $ |
| A less than B | Subtraction | $ B - A $ |

> 🔁 Always reverse order for "less than"!

---

Let me know if you'd like this formatted as a completed worksheet!