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The image contains a projection slide with steps involving solving an algebraic expression or problem. I'll extract the text to analyze it and explain further. The content appears to involve simplifying or solving algebraic expressions.

Here's the extracted text:

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**TRANSFORM RATIONAL PHRASE INTO AN ALGEBRAIC EXPRESSION:**
1. One-quarter of the square of \( b \).
2. Subtract 4 from the square of \( a \) and \( b \).
3. One-half times \( a \) subtracted by \( 5 \).
4. \( 4^{th} \) place divided by 5.
5. The difference between the square of 8 and one-quarter.

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Let me explain the steps of these transformations in algebraic terms:

1. **One-quarter of the square of \( b \)**:
   - This can be written as \( \frac{1}{4}b^2 \).

2. **Subtract 4 from the square of \( a \) and \( b \)**:
   - Assuming we subtract 4 from both squares, it can be expressed as \( a^2 - 4 \) and \( b^2 - 4 \). However, if it's a combined term, it could be interpreted as \( a^2 + b^2 - 4 \).

3. **One-half times \( a \), subtracted by 5**:
   - This is \( \frac{1}{2}a - 5 \).

4. **\( 4^{th} \) place divided by 5**:
   - Without context, this could refer to a number divided by 5, for example, \( \frac{4}{5} \).

5. **The difference between the square of 8 and one-quarter**:
   - The square of 8 is 64, and one-quarter is \( \frac{1}{4} \). The difference is \( 64 - \frac{1}{4} \), or \( \frac{255}{4} \).

Would you like to go over each step in more detail or apply these to specific algebraic problems?

Here are 5 related questions to expand your understanding:
1. How would you combine squares of multiple variables into a single expression?
2. What is the general process for converting word problems into algebraic expressions?
3. Can you find other real-life scenarios where these transformations might apply?
4. How would you simplify expressions involving fractions and powers simultaneously?
5. How can differences between squares, such as in the last example, be useful in solving equations?

**Tip:** Always carefully interpret word problems by breaking them into smaller steps and translating each part into algebraic symbols.

Transform rational phrase into an algebraic expression based on the provided slide.

Explore how to transform rational phrases into algebraic expressions. This guide covers algebraic concepts such as exponents, fractions, and quadratic expressions, suitable for students in Grades 8-10.

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