Practice converting verbal phrases into algebraic expressions with this comprehensive 20-problem worksheet.

It looks like you've uploaded an image of a worksheet titled "Translating Expressions" that asks students to convert verbal phrases into algebraic expressions. Since I can't view images directly, I’ll help you solve the problems based on the text you’ve provided.

Let me go through each problem and translate the verbal expressions into algebraic expressions step by step. Here's the list of problems from your worksheet:

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1. A number increased by 24

- Let the number be $ x $
- Increased by 24 means add 24
- Answer: $ x + 24 $

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2. Triple the amount

- "Triple" means multiply by 3
- Let the amount be $ x $
- Answer: $ 3x $

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3. 6 less than a number

- "Less than" means subtraction, but note: it's 6 less than a number, so we subtract 6 from the number
- Let the number be $ x $
- Answer: $ x - 6 $

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4. A number less than 6

- This is tricky: “a number less than 6” means the number is smaller than 6, but in expression form, it’s usually written as:
- If we let the number be $ x $, then: $ x < 6 $
- But if this is asking for an expression (not inequality), perhaps it means “6 minus a number”
- However, standard interpretation: “A number less than 6” = $ 6 - x $
- Answer: $ 6 - x $

> ⚠️ Note: This depends on context. If it's asking for an expression, $ 6 - x $ is correct. If it's asking for an inequality, $ x < 6 $. Based on the rest of the worksheet, likely $ 6 - x $

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5. 14 raised

- “Raised” typically means exponentiated. But without a power specified, this might mean “raised to a power,” or possibly just “increased.” But “14 raised” is ambiguous.
- More likely, it's meant to be “14 raised to a power,” but since no power is given, maybe it's a typo.
- Alternatively, perhaps it's “14 raised to the second power”? But not specified.
- Assuming it's just “14 squared” or “14 to the power of something” — but no variable given.
- Wait — looking at #7: “Seven times a number to the 4th power” — so likely #5 is incomplete.

Wait — actually, #5 says: “14 raised” — probably missing information. Maybe it's supposed to be “14 raised to the power of a number”? Or “14 raised by a number”?

But #6 says: “14 squared reduced by 42” — so maybe #5 is just “14 raised to the power of x”?

But it's written as “14 raised” — too vague.

Possibility: It might be a typo, and should be “14 raised to the power of a number” → $ 14^x $

But without more info, we can't know.

Alternatively, maybe “raised” means “increased”, so “14 raised by a number” → $ 14 + x $

But again, unclear.

Given ambiguity, let’s assume it's a typo and intended to be “14 raised to the power of a number” → $ 14^x $

But better to check surrounding problems.

Wait — #6: “14 squared reduced by 42” → $ 14^2 - 42 $

So #5: “14 raised” — likely meant to be “14 raised to the power of a number” → $ 14^x $

But since it's not clear, maybe it's just “14” — but that doesn’t make sense.

Alternatively, could be “14 raised by x” → $ 14 + x $

But again, ambiguous.

Let’s move on and come back.

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6. 14 squared reduced by 42

- 14 squared = $ 14^2 $
- Reduced by 42 = subtract 42
- Answer: $ 14^2 - 42 $

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7. Seven times a number to the 4th power

- Let the number be $ x $
- To the 4th power: $ x^4 $
- Seven times that: $ 7x^4 $
- Answer: $ 7x^4 $

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8. The product of 9 and the sum of 4 and 2

- Sum of 4 and 2: $ 4 + 2 = 6 $
- Product of 9 and that sum: $ 9 \times (4 + 2) $
- But since it's symbolic, keep it as: $ 9(4 + 2) $
- But if it's asking for expression, it's $ 9(4 + 2) $, which simplifies to 54
- But likely they want the expression: $ 9(4 + 2) $

Wait — but “the sum of 4 and 2” is constant, so it’s just $ 9(4+2) = 54 $

But maybe it's meant to be “the sum of 4 and a number”?

But it says “sum of 4 and 2” — both numbers.

So: $ 9(4 + 2) = 54 $

But if it's an expression, write it as: $ 9(4 + 2) $

Or simplify: $ 54 $

But since others involve variables, maybe typo?

Wait — perhaps it's “the product of 9 and the sum of 4 and a number”?

But it says “4 and 2”

So unless it's a trick, it's just $ 9(4 + 2) = 54 $

But likely, they want the expression: $ 9(4 + 2) $

Answer: $ 9(4 + 2) $

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9. Half a number plus 10

- Let the number be $ x $
- Half: $ \frac{1}{2}x $
- Plus 10: $ \frac{1}{2}x + 10 $
- Answer: $ \frac{1}{2}x + 10 $

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10. 8 increased by half a number

- Let the number be $ x $
- Half a number: $ \frac{1}{2}x $
- 8 increased by that: $ 8 + \frac{1}{2}x $
- Answer: $ 8 + \frac{1}{2}x $

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11. A person's age 12 years from now

- Let current age be $ x $
- 12 years from now: $ x + 12 $
- Answer: $ x + 12 $

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12. Sixty-eight less than twice a number

- Let the number be $ x $
- Twice: $ 2x $
- Less than: so 68 less than $ 2x $ → $ 2x - 68 $
- Answer: $ 2x - 68 $

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13. How many hours will it take a student to complete her homework?

- This is a question, not a phrase to translate.
- But the instruction is to “translate expressions,” so maybe this is a prompt for a different type of problem?
- But it’s listed among others — likely a mistake.
- Perhaps it's meant to be “The number of hours it takes a student to complete her homework” → let $ h $ be the number of hours → $ h $
- But no operation mentioned.
- So maybe just $ h $, or it's not a translation problem.

But since it's labeled as #13, perhaps it's a misplacement.

Let’s skip for now.

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14. Mrs. Weber has three times the amount of class time as Coach Randall

- Let Coach Randall’s class time be $ r $
- Mrs. Weber has three times that: $ 3r $
- Answer: $ 3r $

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15. High has ten less than three times as many golf balls as Luke

- Let Luke’s golf balls be $ l $
- Three times as many: $ 3l $
- Ten less than that: $ 3l - 10 $
- Answer: $ 3l - 10 $

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16. Samantha has one-third the amount of cars as Jane

- Let Jane’s cars be $ j $
- One-third of that: $ \frac{1}{3}j $
- Answer: $ \frac{1}{3}j $

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17. Monday she runs half as far as she did on Sunday

- Let Sunday’s distance be $ s $
- Half as far: $ \frac{1}{2}s $
- Answer: $ \frac{1}{2}s $

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18. Mr. Lee has 5 less basketballs than Ann

- Let Ann’s basketballs be $ a $
- 5 less than Ann: $ a - 5 $
- Answer: $ a - 5 $

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19. If we paid $125 entrance fee plus $5 per student to go to Chateau Park

- Let number of students be $ s $
- Entrance fee: $125
- $5 per student: $ 5s $
- Total cost: $ 125 + 5s $
- Answer: $ 125 + 5s $

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20. We need to pay $15 per student going to the science center

- Let number of students be $ s $
- Cost: $ 15s $
- Answer: $ 15s $

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Now, back to the problematic ones:

#5: “14 raised”

- Likely a typo. Probably meant to be “14 raised to the power of a number” → $ 14^x $
- Or “14 raised by a number” → $ 14 + x $
- Given #6 is “14 squared reduced by 42”, perhaps #5 is “14 raised to the power of x” → $ 14^x $
- Best guess: $ 14^x $

#13: “How many hours will it take...?”

- Not a phrase to translate into expression; it's a question.
- Possibly a mistake in the worksheet.
- Maybe it was meant to be: “The number of hours it takes a student to complete homework” → $ h $
- But no operation, so just $ h $
- Answer: $ h $ (if allowed)

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Final Answers:

| Problem | Expression |
|--------|------------|
| 1 | $ x + 24 $ |
| 2 | $ 3x $ |
| 3 | $ x - 6 $ |
| 4 | $ 6 - x $ |
| 5 | $ 14^x $ *(assumed)* |
| 6 | $ 14^2 - 42 $ |
| 7 | $ 7x^4 $ |
| 8 | $ 9(4 + 2) $ or $ 54 $ |
| 9 | $ \frac{1}{2}x + 10 $ |
| 10 | $ 8 + \frac{1}{2}x $ |
| 11 | $ x + 12 $ |
| 12 | $ 2x - 68 $ |
| 13 | $ h $ *(assumed)* |
| 14 | $ 3r $ |
| 15 | $ 3l - 10 $ |
| 16 | $ \frac{1}{3}j $ |
| 17 | $ \frac{1}{2}s $ |
| 18 | $ a - 5 $ |
| 19 | $ 125 + 5s $ |
| 20 | $ 15s $ |

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Summary of Key Concepts:

- "Increased by" → addition
- "Less than" → subtraction (order matters: "6 less than x" = $ x - 6 $)
- "Times" → multiplication
- "Squared" → exponent of 2
- "Half" → $ \frac{1}{2} $
- "Twice" → $ 2 \times $
- "One-third" → $ \frac{1}{3} $
- "Reduced by" → subtraction
- "Plus" → addition

Let me know if you'd like these rewritten with specific variables or if there are any corrections needed!