Problem 96 - Algebra for College Students

Question

Answer the question with an algebraic expression. The perimeter of a square is \(i\) inches. What is the perimeter expressed in feet?

Step-by-Step Solution

Answer

\(\frac{i}{12}\) feet

Step 1: Convert Inches to Feet

Since there are 12 inches in a foot, to express the perimeter in feet, we need to divide the number of inches by 12.

Step 2: Set Up the Algebraic Expression

The perimeter of the square is given as \(i\) inches. To convert this to feet, the perimeter in feet is \(\frac{i}{12}\).

Step 3: Simplify the Expression

The expression \(\frac{i}{12}\) cannot be simplified further algebraically in this context, as \(i\) represents any perimeter in inches. Thus, \(\frac{i}{12}\) feet is the final expression for the perimeter.

Key Concepts

Converting Units

Converting units is an essential skill in mathematics, especially when dealing with measurements in different systems, such as the imperial system used in the United States. This concept allows us to express measurements in the units we want. Let's take inches and feet as an example.

• 1 foot equals 12 inches, which is important to remember when converting.
• To convert inches to feet, simply divide the number of inches by 12.
• This conversion is very common when dealing with problems related to length and ensures consistency when solving real-world problems.

In the original problem, the perimeter is given in inches, and our task is to convert it to feet. By understanding how to divide by 12, we can translate our measurement quickly and accurately.

Perimeter of a Square

The perimeter of a square is one of the basic concepts in geometry. It's the total length of all four sides.

• A square has four equal sides. Therefore, the perimeter is calculated by multiplying the length of one side by 4.
• The formula for the perimeter of a square is given by:

  Perimeter = 4 	imes 	ext{side length}

In algebraic terms, if each side of the square is represented by the same variable, say, a length of \( i \) inches, then the perimeter can be expressed simply as \( 4i \) inches. However, if the perimeter itself is given as \( i \) inches, the value already accounts for the entire four sides, so no multiplication is necessary when planning to convert or further evaluate.

Simplifying Expressions

Simplifying expressions in algebra involves reducing them to their most concise and understandable form. This doesn't mean changing the value, just the way it's presented.

• In the given problem, our expression started as \( \frac{i}{12} \), representing the perimeter of a square in feet.
• To simplify means checking if the expression can be reduced further.
• In the context of the problem, \( i \) is an unknown, so we can't simplify \( \frac{i}{12} \) further without additional information.

Simplifying expressions becomes more intricate with more complex algebraic forms but remains a fundamental part of finding clear, efficient solutions to problems. Understanding when an expression is as simple as possible is key to mastering algebra.