Problem 35 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ 20-(-8) $$

Step-by-Step Solution

Answer

The value is 28.

Step 1: Identify the Expression

The expression given is: \( 20 - (-8) \). Recognize that we have a subtraction involving a negative number.

Step 2: Simplify Double Negatives

When you subtract a negative number, it is equivalent to adding the absolute value of that number. Thus, \( 20 - (-8) \) becomes \( 20 + 8 \).

Step 3: Perform the Addition

Add the two numbers from the simplified expression: \( 20 + 8 \).

Step 4: Calculate the Sum

Calculate the sum \( 20 + 8 = 28 \).

Step 5: Verify with a Calculator

Use a calculator to check the result: enter \( 20 - (-8) \) or \( 20 + 8 \) and verify if the display shows 28.

Key Concepts

Subtraction of Negative Numbers

When you first look at the expression \( 20 - (-8) \), it can be a bit confusing because of the double negative situation. Subtracting a negative number may sound complex, but it actually simplifies to an addition. Here's why:

Imagine you owe a friend 8 dollars (represented by -8). If you "subtract the debt," it means you no longer owe that amount. Thus, subtracting a negative is like giving yourself that amount, equivalent to adding 8. Hence:

• Subtracting \(-8\) is the same as adding 8.
• \( 20 - (-8) \) simplifies to \( 20 + 8 \).

This concept is crucial in basic arithmetic because it helps in understanding that subtracting a negative equals a positive addition.

Simplifying Expressions

Simplifying expressions is about making them easier to work with. In the original exercise, the expression \( 20 - (-8) \) was transformed into \( 20 + 8 \). This step is vital because:

• It enhances readability of the expression.
• Makes it easier to solve by turning subtraction into a straightforward addition.

By rewriting double negatives as positive additions, like in our example, arithmetic operations become more intuitive. Simplifying complex expressions can transform daunting calculations into simple tasks.

Using a Calculator for Verification

Using a calculator can be an excellent way to verify your math work, ensuring accuracy in your computations. After calculating \( 20 - (-8) \) and simplifying it to \( 20 + 8 = 28 \), checking your work with a calculator is the final reassurance. To do this:

• Input \( 20 - (-8) \) directly into your calculator.
• Alternatively, you can enter \( 20 + 8 \) to see the same result.

The calculator should display 28, which confirms your manual calculations. This verification step not only boosts confidence in your arithmetic skills but also minimizes errors in more complex math problems. Remember, a calculator is a tool to confirm the accuracy of your work.