Translating Algebraic Phrases (Simple Version) (A) - Free Printable

It looks like you've uploaded an image of a completed worksheet titled "Translating Algebraic Phrases (A) Answers" from Math-Drills.com. This worksheet contains 20 algebraic phrases, each with its corresponding algebraic expression written in the answer column.

Since this is already a solution sheet, it appears that the task was to translate verbal phrases into algebraic expressions, and the answers are provided.

However, if your goal is to understand how to solve these types of problems, I can walk you through the logic behind each type of phrase and explain how to translate them into algebraic expressions.

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🔍 General Rules for Translating Phrases to Algebraic Expressions:

| Phrase | Operation |
|-------|-----------|
| "sum of", "plus", "increased by" | Addition (+) |
| "difference between", "subtracted from", "minus" | Subtraction (−) |
| "product of", "times", "multiplied by" | Multiplication (× or ·) |
| "quotient of", "divided by" | Division (÷ or /) |
| "a number" | Use a variable (e.g., *x*, *n*, *p*) |
| "to the power of" | Exponentiation (e.g., $ x^n $) |

Let’s go through a few examples from the worksheet to demonstrate how to interpret and write the expressions:

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✔ Example 1:

Phrase: *a number b divided by thirty-six*
Expression: $ \frac{b}{36} $

- "a number b" → variable: *b*
- "divided by thirty-six" → divide *b* by 36

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✔ Example 2:

Phrase: *sixty-six subtracted from a number p*
Expression: $ p - 66 $

- "a number p" → *p*
- "sixty-six subtracted from..." → *p minus 66*

> ⚠️ Note: "Subtracted from" means the number comes first. So "66 subtracted from p" = $ p - 66 $, not $ 66 - p $.

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✔ Example 5:

Phrase: *three divided by a number g*
Expression: $ \frac{3}{g} $

- "three" → 3
- "divided by a number g" → $ \frac{3}{g} $

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✔ Example 10:

Phrase: *a number y multiplied by fifty-six*
Expression: $ 56y $

- "a number y" → *y*
- "multiplied by fifty-six" → $ 56 \times y $ → written as $ 56y $

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✔ Example 12:

Phrase: *twenty-nine to the w³ power*
Expression: $ 29^{w^3} $

- "twenty-nine" → 29
- "to the w³ power" → exponent is $ w^3 $
- So: $ 29^{w^3} $

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✔ Example 18:

Phrase: *a number u to the power of sixty-five*
Expression: $ u^{65} $

- "a number u" → *u*
- "to the power of sixty-five" → $ u^{65} $

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✔ Example 20:

Phrase: *the product of fifty-two and a number c*
Expression: $ 52c $

- "product of" → multiplication
- 52 × *c* → $ 52c $

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📌 Summary:

All the answers on the sheet are correct based on standard algebraic translation rules. Here's a quick review of key points:

- Always identify the operation based on keywords.
- Pay attention to order — especially with subtraction and division.
- Variables represent unknown numbers.
- Use proper notation: fractions for division, exponents for powers, etc.

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