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Chapter 6: Problem 52

Evaluate the expression. $$ \frac{x}{15} \text { when } x=30 $$

Short Answer

Expert verified
The evaluated result of the expression is 2.

Step by step solution

01

Understand the expression.

The expression given is \(\frac{x}{15}\). This implies that the value of \(x\) has to be divided by 15.
02

Substitute the value of x

According to the exercise, \(x = 30\). Hence, we replace \(x\) in the expression by 30. This changes the expression to \(\frac{30}{15}\).
03

Solve the expression

After substituting, we need to solve \(\frac{30}{15}\). By using the basic division, we get the result as 2.

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Key Concepts

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

Evaluate Expression
When we're asked to evaluate an expression, our goal is to find the value of that expression by performing the operations indicated. An expression isn't a full equation with two sides, but rather, it's a mathematical phrase that can include numbers, variables, and operators (like addition or division). In our example, the expression is \( \frac{x}{15} \). This tells us we need to take the value of \( x \) and divide it by 15.
Evaluating expressions is a common task in math, helping us determine the specific outcome based on the given values. To evaluate any expression, follow these steps:
  • Identify the expression to be evaluated.
  • Understand the operations involved.
  • Substitute known values for any variables.
  • Perform the operations to find the value.
Remember, each operator in an expression has a specific role, guiding us to the final answer.
Substitution
Substitution is a crucial step in evaluating expressions, especially when they contain variables. In our context, substitution involves replacing a variable with a specific number provided in the exercise. This allows us to calculate the expression's value with actual numbers instead of placeholders. For the given exercise, we're told that \( x = 30 \). This means you substitute 30 in place of \( x \) in the expression \( \frac{x}{15} \).
Here's how substitution works effectively:
  • Identify the variable in the expression, which is \( x \) in this case.
  • Replace the variable with the given number, changing \( \frac{x}{15} \) to \( \frac{30}{15} \).
  • Ensure the substitution is correct and aligns with the mathematical context.
Substitution turns abstract expressions into concrete problems we can solve, making it an essential math skill.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. They are foundational to many mathematical problems. In our exercise, we're focusing on the division operation. After substituting \( x = 30 \), we're left with \( \frac{30}{15} \), which is a division problem.
To solve \( \frac{30}{15} \) using division:
  • Recognize that the expression \( \frac{30}{15} \) means '30 divided by 15'.
  • Perform the division operation: 30 divided by 15 equals 2.
Understanding division is essential because it's frequently used in solving fraction-based expressions and equations. It helps in breaking down larger numbers into simpler parts, and when paired with other arithmetic operations, it expands our ability to tackle more complex mathematical challenges.

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