Problem 45 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$-2.06-(-2.06)$$

Step-by-Step Solution

Answer

The result is \( 0.00 \).

Step 1: Understanding Negative numbers subtraction

When subtracting a negative from a negative number, this essentially changes to addition. Conceptually, if we move in a negative direction, and then subtract a negative, it means we will be moving back in the positive direction. Therefore, \( -2.06 - (-2.06) \) becomes \( -2.06 + 2.06 \).

Step 2: Perform Addition

Adding \( -2.06 \) and \( 2.06 \) gives result equals to \( 0.00 \).

Key Concepts

Negative Numbers

Negative numbers represent values less than zero. They are the opposite of positive numbers. You can think of them like temperatures below freezing or debts in a bank account. For example, if it's 3 degrees below zero, you would write that as \(-3\). Similarly, having a debt of 5 dollars means you are \(-5\) dollars below having zero dollars. Negative numbers appear to the left of zero on the number line.

• If you add negative numbers, you're essentially moving to the left on the number line.
• Conversely, if you subtract them, you may move to the right, depending on the operation.

Understanding negative numbers is crucial before advancing to more complex arithmetic like subtraction and addition of negative numbers.

Addition of Negative Numbers

Adding negative numbers can seem tricky at first. However, it becomes straightforward when you consider the number line perspective. For instance:

• If you add \(-3\) and \(-2\), think of starting at zero, moving left to \(-3\), and then moving left again by \(-2\). This lands you at \(-5\).
• When adding a larger negative number to a smaller positive one, you effectively subtract the smaller from the larger and keep the negative sign. For example, \(5 + (-3) = 2\).

In essence, to add two negative numbers together, you add their absolute values and keep the negative sign. This is particularly important in scenarios requiring consistent direction measurement, like debts, where more debt (negative) results in a larger negative.

Basic Algebra

Basic algebra allows us to work with numbers in a generalized way. This involves using letters or symbols (like \(x\) or \(y\)) to represent numbers in equations or expressions. One key aspect in algebra is understanding operations like addition and subtraction, even with negative numbers.

• When faced with expressions such as \(-x - (-y)\), the rules of arithmetic apply—subtracting a negative is the same as adding the positive. For example, \(-2.06 - (-2.06)\) translates to \(-2.06 + 2.06\).
• Evaluating expressions requires performing operations carefully according to the order of operations and managing the signs of numbers correctly.

Algebra is a powerful tool that helps us understand the relationships between numbers, enabling us to solve equations and predict outcomes. Comprehending these basics is essential for tackling more sophisticated algebraic concepts later.