Problem 26 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ -5-(-3) $$

Step-by-Step Solution

Answer

The result of \(-5 - (-3)\) is \(-2\).

Step 1: Identify the Expression

The problem requires us to perform the subtraction operation on the expression \(-5 - (-3)\).

Step 2: Simplify the Expression

When subtracting a negative number, it is equivalent to adding the positive version of that number. Thus, \(-5 - (-3)\) becomes \(-5 + 3\).

Step 3: Perform the Addition

Add \(-5\) and \(3\) together. This involves moving 3 units to the right on the number line from -5, which gives us \(-2\).

Step 4: Verify with a Calculator

Check the result using a calculator: input \(-5 + 3\) into your calculator and confirm that it equals \(-2\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus (-) sign. They are common in many real-life scenarios, such as temperatures below freezing or financial debts. Understanding negative numbers is crucial for various arithmetic operations, especially when involving subtraction.

Here are a few key points about negative numbers:

• They are usually found to the left of zero on a number line.
• When a negative number is subtracted, it can be visualized as moving in the opposite direction on a number line, leading to addition.
• Comparing negative numbers, the one with a smaller absolute value is actually larger (e.g., -3 is greater than -5).

Grasping these concepts helps you handle more complex problems involving negative numbers more comfortably.

Arithmetic Operations

Arithmetic operations encompass the basic functions of math, including addition, subtraction, multiplication, and division. Subtraction is one of these key operations and involves finding the difference between numbers. In particular, subtracting negative numbers requires an understanding of how these operations interact.

When subtracting, if one of the numbers is negative, you can simplify the operation by converting it into addition. For example, \(-5 - (-3)\) turns into \(-5 + 3\). This transformation occurs because subtracting a negative is equivalent to adding its positive counterpart. Essentially, two negatives cancel each other out to make a positive. This rule is pivotal in simplifying expressions and making calculations easier.

• Always remember that subtracting a negative number turns into addition.
• Ensure to double-check your changes to conversions, as it can affect the final result.

Using Calculators in Math

Using a calculator can be an incredibly helpful step in verifying the results of arithmetic operations, especially with decimals or large numbers. Calculators allow students to confirm their manual calculations, ensuring accuracy. Let's see why and how they are useful:

• They save time and reduce computation errors.
• For checks, entering the simplified expression (such as \(-5 + 3\) instead of \(-5 - (-3)\)) is essential to avoid errors.
• Calculators also provide immediate feedback, which is helpful for learning and correcting mistakes.

Although calculators are powerful tools, they should be used to complement, not replace, the understanding of arithmetic operations. Building a strong foundation in math logic ensures better problem-solving skills beyond just obtaining the correct answer.