Plumbing Mathematics Reference Sheet | PDF | Area | Gallon - Free Printable

The image you've uploaded is a page from a plumbing mathematics reference guide, specifically focusing on how to solve mathematical problems using a step-by-step method. It includes an example problem involving calculating the area of a roof, and it walks through the process using four steps.

Let’s go through the content and solve the example problem, then explain the solution clearly.

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🔧 Problem:

> What is the area of a roof 120 inches wide and 20 feet 6 inches long?

Options:
- (A) 200 square feet
- (B) 205 square feet
- (C) 210 square feet
- (D) 215 square feet

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✔ Step-by-Step Solution Using the Given Method

#### STEP 1: Write the applicable formula.

We are calculating the area of a rectangle, so we use:

> Area = Length × Width
> or
> A = L × W

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#### STEP 2: Substitute the numerical value for each symbol in the formula.

Given:
- Width = 120 inches
- Length = 20 feet 6 inches

So:
> Area = (20 ft 6 in) × (120 in)

But we need consistent units — both dimensions must be in the same unit before multiplying.

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#### STEP 3: Change values to like units.

We'll convert everything to feet because the answer choices are in square feet.

##### Convert width from inches to feet:
- 120 inches ÷ 12 = 10 feet

##### Convert length from feet and inches to feet:
- 20 feet 6 inches = 20 + (6 ÷ 12) = 20 + 0.5 = 20.5 feet

Now:
> Area = 20.5 ft × 10 ft

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#### STEP 4: Solve the problem and label your answer.

> 20.5 × 10 = 205 square feet

✔ So, the area is 205 square feet.

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🟩 Answer: (B) 205 square feet

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🔍 Explanation Summary:

1. Formula: Use the rectangle area formula: A = L × W.
2. Units Matter: Since one dimension is in inches and the other in feet, convert both to the same unit.
- 120 inches = 10 feet
- 20 ft 6 in = 20.5 feet
3. Multiply: 20.5 × 10 = 205
4. Label: Answer is in square feet, as required.

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💡 Key Takeaway:

Always follow the four-step method:
1. Formula
2. Substitution
3. Unit conversion
4. Solve and label

This ensures accuracy, especially when dealing with mixed units (like feet and inches), which are common in plumbing and construction.

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✔ Final Answer: (B) 205 square feet