Problem 27 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ -11-(-8) $$

Step-by-Step Solution

Answer

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

Step 1: Identify the Operation

The problem requires you to find the difference between two numbers: -11 and -8. In subtraction, you subtract the second number from the first number.

Step 2: Apply the Subtraction Rule for Negative Numbers

When subtracting a negative number, you actually add the absolute value of that number. Thus, -11 - (-8) becomes -11 + 8.

Step 3: Perform the Addition

Now, you need to add the two numbers: -11 and 8. Starting from -11, add 8. This is equivalent to moving 8 steps towards a positive number on the number line, which gives the result -3.

Step 4: Verify with a Calculator

To ensure accuracy, use a calculator to compute -11 - (-8). Enter it as -11 + 8 and verify that the result is indeed -3.

Key Concepts

Negative Numbers

Working with negative numbers might feel like visiting the opposite side of the world, but it's not as complex once you understand the basics. Negative numbers are numbers less than zero, often thought of as owing something, as in negative money, or being below sea level. Imagine a thermometer: temperatures above zero are positive, while those below are negative.

In subtraction involving negative numbers, such as in our exercise, you often encounter scenarios like "subtracting a negative number." When this happens, you're actually "adding the opposite." So in the case of \(-11 - (-8)\), you're really adding \(8\) to \(-11\). Keep this rule in mind, and you'll find handling negative numbers in subtraction much easier!

Absolute Value

The concept of absolute value deals with how far a number is from zero on the number line, regardless of direction. It simplifies scenarios where you're dealing with both negative and positive numbers. Absolute value is often represented by two vertical lines, like this: \(|-x|\). For example, \(|-8|\) and \(8|\) both have an absolute value of \(8\).

So why is this concept crucial for subtraction problems involving negative numbers? When you subtract a negative number, it's like adding its absolute value to the original number. That's why \(-11 - (-8)\) turns into \(-11 + 8\). By thinking of the absolute value, you're focusing on the size of the steps you're adding or subtracting, not the direction.

• Use absolute value to "flip" the negative before performing operations.
• This makes calculations simpler and less error-prone.

Calculator Verification

A calculator can be a reliable friend when verifying mathematical operations, especially when dealing with negative numbers, which can trip you up easily if not careful. Here's how you can double-check your work:

To verify \(-11 - (-8)\), you should remember that this translates to \(-11 + 8\). Enter this into your calculator to check if the result matches your manual calculation. This verification is vital for ensuring accuracy and building confidence in your math skills.

• Always input negative numbers carefully, using the negative sign clearly distinguished.
• For subtraction of negatives, ensure you're adding the absolute value instead.
• Cross-check your answers by seeing if the calculated result reflects your expectations.