Problem 62 - Prealgebra and Introductory Algebra

Question

Evaluate the expression \(x-y\) for the given values of \(x\) and \(y.\) $$x=-3.69, y=-1.527$$

Step-by-Step Solution

Answer

-2.163

Step 1: Identify the Given Values

Given, \(x = -3.69\) and \(y = -1.527\).

Step 2: Substitute the values into the expression

Plug these values into the expression \(x - y\). It becomes \((-3.69) - (-1.527)\). Remember that subtracting negative numbers is the same as adding positive numbers.

Step 3: Simplify the expression

The expression simplifies to \(-3.69 + 1.527\).

Step 4: Calculate the Result

By performing the addition, the result of \(-3.69 + 1.527\) is \(-2.163\).

Key Concepts

Evaluating Expressions

Evaluating expressions involves replacing variables with their given numbers and simplifying the result. This process is crucial to understand because it forms the basis of solving algebraic problems.
In the given problem, we start by identifying the values for the variables. Here, you're given that \(x = -3.69\) and \(y = -1.527\).
To evaluate the expression \(x - y\), you need to:

• Substitute the known values for \(x\) and \(y\) into the expression.
• Replace \(x\) with \(-3.69\) and \(y\) with \(-1.527\).
• This transforms the expression to \((-3.69) - (-1.527)\).

Handling numbers in expressions accurately leads to the correct answer. Practicing these steps builds a strong foundation for tackling more complex algebraic operations.

Subtraction

Subtraction is a core operation in mathematics where you take one number away from another. It is especially important to understand subtraction involving negative numbers.
In the exercise, subtraction is presented as \((-3.69) - (-1.527)\).
When you subtract a negative number, remember that it turns into addition. This is because subtracting a negative is the same as adding its positive counterpart.
Therefore, the expression simplifies by:

• Recognizing \((-3.69) - (-1.527)\) changes to \(-3.69 + 1.527\).

This transformation is key to finding the right solution. Understanding this concept is essential for accurately solving mathematical equations that include a subtraction of negative numbers.

Negative Numbers

Negative numbers can sometimes seem tricky, especially when they're involved in operations like subtraction. A negative number represents a value less than zero.
In this problem, both \(x\) and \(y\) are negative. They appear in the expression handling subtraction.\
Here's how you manage operations:

• A negative sign before a number indicates that the number is less than zero, like \(-3.69\) and \(-1.527\).
• When subtracting, consider the rules of signs. Subtracting a negative essentially becomes adding its absolute value.

Therefore, when you see \((-3.69) - (-1.527)\), it simplifies to adding these numbers as \(-3.69 + 1.527\). By simplifying you focus on the absolute change instead of getting bogged down by signs.
By knowing these principles, you'll more easily navigate problems that involve negative numbers and subtraction.