Problem 41 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$-3.1-(-1.1)$$

Step-by-Step Solution

Answer

The result of the given subtraction is -2.0.

Step 1: Understand the Problem

The problem is a simple subtraction: \(-3.1 - (-1.1)\). Notice that there are two negative signs which means this subtraction adds up to an addition.

Step 2: Change the Subtraction to Addition

To make it easier, the problem can be rewritten as an addition by changing \(- (-1.1)\) to \(+1.1\). Thus, the problem changes to \(-3.1 + 1.1\).

Step 3: Perform the Addition

Now, add -3.1 and 1.1. This equals to -2.0.

Key Concepts

Understanding Negative Numbers

Negative numbers can be a bit tricky at first, but they simply represent values less than zero. When we deal with negative numbers, we move to the left on the number line. For example,

• -1 is one unit to the left of 0,
• -2 is two units left,
• and so on.

Negative numbers are commonly represented with a minus sign \((-\)). When subtracting a negative number, it may feel confusing at first. But keep in mind that subtracting a negative is the same as adding a positive, because the two minus signs turn into a positive one. In our example, subtracting \(-3.1 - (-1.1)\) translates to \(-3.1 + 1.1\). This is a fundamental idea to grasp when dealing with negative numbers. Subtraction and addition involving negative numbers can sometimes be seen as a game of perspective on the number line. Understanding the direction you move in makes solving these problems intuitive and straightforward.

Adding Negative and Positive Numbers

Addition with negative numbers involves movement on the number line too. When you add negative and positive numbers, you're essentially balancing between left and right on the number line. Let's consider our example of \(-3.1 + 1.1\). Imagine starting at -3.1 on the number line.

• The addition of 1.1 requires you to move to the right.
• Moving right by 1.1 brings you to -2.0.

This process illustrates how addition of negative and positive numbers is really about finding the balance point between them on the number line.A handy tip is to view the operation in terms of their individual signs:

• Add a negative: Move to the left.
• Add a positive: Move to the right.

As you become more familiar with these operations, you'll find that visualizing movements on the number line can help simplify and quickly solve problems.

The Role of Integers

Integers are a core building block in mathematics. They include all whole numbers and their negative counterparts. Yes, zero counts among them too! Understanding integers is crucial when solving equations involving subtraction or addition.For example, integers help us:

• Distinguish clearly between positive, negative numbers, and zero.
• Understand the complete set of numbers useful for basic arithmetic operations.

In the context of our exercise, while \(-3.1\) is actually a decimal, the integer skills help us handle the sign in front of the number. Remember, integer operations set the rules we follow when we turn subtraction operations into additions.As you encounter different mathematical problems, knowing how to manage integers will strengthen your ability to tackle subtraction and addition with ease. The rules and properties of integers serve as your guide throughout many arithmetic adventures.