91Ó°ÊÓ

Evaluating expressions is like unlocking a puzzle with numbers and variables! It's how we find a specific numerical value for a mathematical expression by substituting variables with given numbers. When faced with a mathematical expression, the goal is to replace letters (or variables) like \( x \), \( y \), and \( z \) with actual numbers. This lets us compute a definitive result.

In our example, we had the expression \( xz - y \). After substituting \( x = 3 \), \( y = -0.2 \), and \( z = 5.7 \) into the expression, it transforms into \( 3 \times 5.7 - (-0.2) \). This is the essence of evaluating expressions—replacing variables and following the order of operations!

It's essential to follow each operation carefully to reach the correct answer.

The substitution method is like a magical bridge that turns variables into numbers! This method involves replacing each variable in an expression with its given value. Let's break it down to understand how it works in practice.

In our specific exercise, the original expression is \( xz - y \). With given values \( x = 3 \), \( y = -0.2 \), and \( z = 5.7 \), the substitution method involves:

• Inserting \( 3 \) wherever \( x \) appears
• Inserting \( -0.2 \) for \( y \)
• Inserting \( 5.7 \) for \( z \)

After substitution, variables vanish, leaving purely numerical expressions for simple calculations. The expression becomes \( 3 \times 5.7 - (-0.2) \). This process seamlessly transforms complex expressions into numbers we can easily handle!

Basic arithmetic operations are essential in revealing the final answer when evaluating expressions. In this context, it includes multiplication and subtraction, which are often encountered in such problems.

Once you substitute and transform variables into numbers, the next step is to execute the arithmetic operations in the correct order:

• Multiplication: First, calculate \( 3 \times 5.7 \), resulting in \( 17.1 \). Multiplication involves combining multiple units into a whole.
• Subtraction (involving negative numbers): Here we encounter \( 17.1 - (-0.2) \). Remember, subtracting a negative is identical to adding a positive. So, \( 17.1 - (-0.2) \) simplifies to \( 17.1 + 0.2 \), leading to a result of \( 17.3 \).

Mastering these operations is key to solving expressions correctly, ensuring you move step by step without skipping any vital procedures.