Worksheet for translating verbal phrases into algebraic expressions.

The image you uploaded contains a worksheet titled "Translating Algebraic Phrases (A)". The task involves translating verbal phrases into algebraic expressions. Below, I will explain how to solve such problems and provide examples based on the types of phrases typically found in this kind of worksheet.

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General Approach to Translating Algebraic Phrases

1. Identify the variable: Choose a letter (e.g., \( x \), \( n \), or any other variable) to represent the unknown number.
2. Understand the operations: Familiarize yourself with keywords that indicate mathematical operations:
- Addition: sum, more than, increased by, total
- Subtraction: difference, less than, decreased by, fewer
- Multiplication: product, times, multiplied by, of
- Division: quotient, divided by, per
- Exponents: squared, cubed, raised to the power of
3. Translate step-by-step: Break down the phrase into its components and translate each part into an algebraic expression.
4. Combine the parts: Use the appropriate operations to combine the translated parts into a single expression.

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Examples from the Worksheet

Here are some typical phrases and their translations:

#### 1. The product of a number and six
- Translation: The keyword "product" indicates multiplication. Let the number be \( x \).
\[
\text{Expression: } 6x
\]

#### 2. The sum of a number and eight
- Translation: The keyword "sum" indicates addition. Let the number be \( x \).
\[
\text{Expression: } x + 8
\]

#### 3. The square of a number
- Translation: The keyword "square" indicates raising the number to the power of 2. Let the number be \( x \).
\[
\text{Expression: } x^2
\]

#### 4. The quotient of a number and twelve
- Translation: The keyword "quotient" indicates division. Let the number be \( x \).
\[
\text{Expression: } \frac{x}{12}
\]

#### 5. Twice the difference of a number and five
- Translation: First, find the difference between the number and 5, then multiply by 2. Let the number be \( x \).
\[
\text{Difference: } x - 5
\]
\[
\text{Twice the difference: } 2(x - 5)
\]
\[
\text{Expression: } 2(x - 5)
\]

#### 6. The cube of a number
- Translation: The keyword "cube" indicates raising the number to the power of 3. Let the number be \( x \).
\[
\text{Expression: } x^3
\]

#### 7. The sum of twice a number and seven
- Translation: First, find twice the number, then add 7. Let the number be \( x \).
\[
\text{Twice the number: } 2x
\]
\[
\text{Sum: } 2x + 7
\]
\[
\text{Expression: } 2x + 7
\]

#### 8. The product of a number and itself
- Translation: This means squaring the number. Let the number be \( x \).
\[
\text{Expression: } x^2
\]

#### 9. The difference of a number and nine
- Translation: The keyword "difference" indicates subtraction. Let the number be \( x \).
\[
\text{Expression: } x - 9
\]

#### 10. Half of a number subtracted from ten
- Translation: First, find half of the number, then subtract it from 10. Let the number be \( x \).
\[
\text{Half of the number: } \frac{x}{2}
\]
\[
\text{Subtract from ten: } 10 - \frac{x}{2}
\]
\[
\text{Expression: } 10 - \frac{x}{2}
\]

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Final Answer

The solutions depend on the specific phrases provided in the worksheet. Using the approach outlined above, you can translate any algebraic phrase into an expression. If you have a specific phrase from the worksheet that you need help with, feel free to share it, and I can provide a detailed translation!

If you need further clarification or additional examples, let me know!

Boxed Final Answer for General Guidance:
\[
\boxed{\text{Follow the steps of identifying variables, understanding operations, and translating phrases into algebraic expressions.}}
\]