Problem 33 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ 8-(-3) $$

Step-by-Step Solution

Answer

The result of \(8 - (-3)\) is 11.

Step 1: Understand the Expression

The expression we need to solve is given as \(8 - (-3)\). This involves subtracting a negative number from another number.

Step 2: Apply the Rule for Subtracting Negatives

When you subtract a negative number, it is equivalent to adding the absolute value of that number. This means \(8 - (-3)\) becomes \(8 + 3\).

Step 3: Perform the Addition

Now, calculate \(8 + 3\). Adding these two numbers results in \(11\).

Step 4: Verify with a Calculator

Use a calculator to confirm the calculation: input \(8 + 3\) and ensure it returns \(11\).

Key Concepts

Understanding Negative Numbers

Negative numbers are values less than zero and are usually represented with a minus sign before them, such as -1, -2, -3, and so on. They are the opposite of positive numbers and lie to the left of zero on the number line. Negative numbers play a crucial role in various mathematical operations and real-world scenarios, like temperature changes and financial calculations.
Understanding how negative numbers work is vital for performing operations that include them. It helps to remember:

• If you have a positive number, you are above zero on the number line.
• If you have a negative number, you are below zero on the number line.

Recognizing the relationship between negative and positive numbers, including their interactions, prepares you for operations involving both types of numbers.

Addition Overview

Addition is one of the basic mathematical operations used to calculate the total or sum when combining numbers. It is the process of finding the total number of items when two or more groups are combined. When working with numbers, addition is typically signified by a plus sign "+".
When dealing with addition:

• Positive numbers increase the total value.
• Negative numbers, when added, can decrease the total value (unless they cancel with a subtraction).

For example, adding a negative number is essentially finding the balance between the positive and negative values, which can lead to either an increase or decrease of the total value depending on the situation. In the exercise, we utilized addition when converting the subtraction of a negative number to the addition of its positive counterpart.

Mathematical Operations Simplified

Mathematical operations include addition, subtraction, multiplication, and division. These operations are fundamental in solving equations and finding solutions to numerical problems. Each of these operations centers around manipulating numbers to reach a conclusion.
When you perform mathematical operations, it's essential to understand the rules that govern them:

• Adding and subtracting negative numbers requires special attention because they affect operations differently from positive numbers.
• Multiplying or dividing negative numbers follows distinct rules: multiplying or dividing two negative numbers returns a positive outcome, while mixing positive and negative returns a negative outcome.

In our exercise example, subtracting a negative number transformed the operation into addition. This change highlights the specific rules that apply and the importance of implementing correct operations, leading us to the correct solution.