5.4 NOTES Condensed - Translating Expressions - Gammache PDF | PDF ... - Free Printable

Let's solve the problem 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 expressions.

| 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 a and b: $ a + b $
> - The DIFFERENCE of a and b: $ a - b $
> - The PRODUCT of a and b: $ a \cdot b $
> - The QUOTIENT of a and b: $ \frac{a}{b} $

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📝 Step 2: Write each verbal phrase as an algebraic expression

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

✔ Answer: $ 8 + t $

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

✔ Answer: $ \frac{g}{15} $

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

✔ Answer: $ 5b $

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#### 4) the difference of 32 and x
→ "difference" means subtraction
→ Important: "of 32 and x" means $ 32 - x $

✔ Answer: $ 32 - x $

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⚠️ KEY WORDS Reminder:

- LESS THAN → subtract the first number from the second → switch order!
- MORE THAN → add the first number to the second

Example given:
> "five dollars less than Jennifer earned"
> Let $ d $ = amount Jennifer earned
> → $ d - 5 $ (not $ 5 - d $)

So, for phrases like “less than,” reverse the order.

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Now solve the rest:

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

✔ Answer: $ x + 8 $

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

✔ Answer: $ p - 6 $

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#### 7) 14 less than f
→ "less than" → reverse order
→ $ 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’s let $ r $ = number of runs Pirates scored
→ "3 more than" → add 3 to $ r $
→ $ 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:

| Problem | Algebraic Expression |
|--------|----------------------|
| 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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🎯 Key Tips Recap:

- Sum → addition (+)
- Difference → subtraction (−), order matters
- Product → multiplication (× or · or just write side-by-side)
- Quotient → division (÷ or fraction)
- Less than → reverse the order (e.g., "5 less than x" → $ x - 5 $)
- More than → add (e.g., "5 more than x" → $ x + 5 $)

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