Worksheet demonstrating how to use proportions to solve part, whole, or percent problems with the percent proportion equation.

It looks like you've uploaded a document titled "Using Proportions to Perform PART Calculations – Notes", which explains how to solve percent problems using the Percent Proportion Equation. Let's go through the content, explain the key concepts, and walk through the example provided.

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🔍 Overview of the Document

The document is a teaching guide that explains how to use proportions to solve percent problems. It focuses on three types of questions:

1. What is X% of Y? (Finding the part)
2. X is what percent of Y? (Finding the percent)
3. X is 10% of what number? (Finding the whole)

But in this case, it’s focusing on finding the part when given the percent and the whole.

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📌 The Percent Proportion Equation

The core formula presented is:

\[
\frac{\text{PART}}{\text{WHOLE}} = \frac{\text{PERCENT}}{100}
\]

This can be written as:

\[
\frac{P}{W} = \frac{P\%}{100}
\]

Where:
- P = Part (unknown or known)
- W = Whole (known or unknown)
- P% = Percent (given as a percentage)

> 💡 Important Rule: "100" always goes in the denominator with the percent.

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✔ Step-by-Step Method

Let’s follow the steps outlined in the document to solve a problem.

#### 🔹 Example: What is 25% of 500?

Step 1: Determine what we are looking for
- We're asked: "What is 25% of 500?"
- So, we are solving for the part.
- We know:
- Percent = 25%
- Whole = 500
- Part = ? (unknown)

Step 2: Substitute into the proportion equation

\[
\frac{P}{500} = \frac{25}{100}
\]

Now, solve for P.

Step 3: Solve the proportion

You can use either:
- Up-and-Down Method (cross-multiplication)
- Cross Product Method

Let’s use cross multiplication:

\[
P \times 100 = 25 \times 500
\]

\[
100P = 12,500
\]

Now divide both sides by 100:

\[
P = \frac{12,500}{100} = 125
\]

✔ So, 25% of 500 is 125.

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🧠 Alternative: Up-and-Down Method

The document shows a visual way to solve proportions:

```
P 25
---- = ----
500 100
```

Then cross multiply:

- Multiply diagonally:
\( P \times 100 = 25 \times 500 \) → same as before

Or, if you’re solving for P, you can think:

\[
P = \frac{25 \times 500}{100} = \frac{12,500}{100} = 125
\]

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🎯 Summary

To solve any percent problem using proportions:

1. Identify what you're solving for: Part, Whole, or Percent.
2. Plug known values into the proportion:
\[
\frac{P}{W} = \frac{P\%}{100}
\]
3. Use cross multiplication to solve for the unknown.

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📝 Final Answer to the Example

> What is 25% of 500?
> Answer: 125

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🔄 Practice Tip

Try this method on other problems:
- What is 10% of 200?
- What is 75% of 80?

You’ll always use the same proportion structure!

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If you have a specific problem from the image you'd like me to solve step-by-step, feel free to describe it!