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Chapter 2: Problem 449

In the following exercises, evaluate each expression. $$ h w \text { when } h=12, w=3 $$

Short Answer

Expert verified
36

Step by step solution

01

Understand the given expression

The given expression is \( h w \). This means you need to multiply the value of \( h \) and the value of \( w \).
02

Substitute the given values

From the exercise, \( h = 12 \) and \( w = 3 \). Substitute these values into the expression: \( 12 \times 3 \).
03

Perform the multiplication

Calculate the product of 12 and 3: \( 12 \times 3 = 36 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is a fundamental concept in algebra. It involves replacing variables in an expression with their given values. This allows you to simplify and evaluate expressions. In our example, we have the expression \( h w \) where \( h = 12 \) and \( w = 3 \). Substitution means we take these values and plug them into the expression. So, \( h w \) becomes \( 12 \times 3 \). This step is crucial because it transforms the algebraic expression into a numerical one that we can calculate directly.
Multiplication
Multiplication is one of the basic arithmetic operations, represented by the symbol \( \times \) or sometimes by a dot \( \cdot \). When we multiply, we are essentially combining groups of equal sizes. In the given exercise, we need to multiply the values obtained after substitution: \( 12 \times 3 \). Here, 12 signifies 12 groups of 3, or vice versa. To perform this multiplication:
  • First, multiply the tens place: \( 10 \times 3 = 30 \)
  • Next, multiply the units place: \( 2 \times 3 = 6 \)
  • Finally, add the two results: \( 30 + 6 = 36 \)
Thus, \( 12 \times 3 \) equals 36.
Variables
Variables are symbols, often letters, used to represent unknown or changeable values in mathematical expressions and equations. They allow us to write formulas and expressions that can be used for various calculations. In our exercise, \( h \) and \( w \) are variables. Before substitution, we don't know their exact values. Once given, these variables can be replaced with specific numbers.
  • Variables make expressions versatile and reusable.
  • They help in setting up equations to solve real-world problems.
  • Understanding how to manipulate variables is essential for solving algebraic equations and expressions.
In summary, variables are key elements in algebra that facilitate general problem-solving.

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Most popular questions from this chapter

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