Problem 62 - Fundamentals of Mathematics

Question

Perform the subtraction \(-8-(-20)\)

Step-by-Step Solution

Answer

The result of \(-8 - (-20)\) is 12.

Step 1: Understanding the Problem

The problem asks us to perform the subtraction of two numbers, -8 and -20, where we are subtracting -20 from -8.

Step 2: Identifying the Subtraction Rule

Recall the rule for subtracting a negative number: Subtracting a negative number is the same as adding its positive counterpart. Therefore, \(-8 - (-20) = -8 + 20\).

Step 3: Performing the Addition

Now, add the numbers -8 and +20 together. This can be thought of as starting at -8 on the number line and moving 20 steps to the right.

Step 4: Calculate the Result

When you add 20 to -8, you reach +12. Therefore, \(-8 + 20 = 12\).

Step 5: Double-Checking the Calculation

Review the steps to ensure accuracy. We converted the subtraction into an addition, added the values correctly, and reached the final answer of 12.

Key Concepts

Negative Numbers

Negative numbers are values that are less than zero. They are represented with a minus sign "-" in front of the number, like -8 or -20. Understanding negative numbers is essential in integer subtraction, as they represent quantities below zero, such as temperatures below freezing or debts. To visualize this, imagine the temperature dropping below zero or as your bank account balance going negative.
Negative numbers stretch to the left of zero on a number line. The further left a number is, the less its value; -20 is less than -8, meaning -20 is further left on the number line than -8. Knowing their position helps comprehend the impact of subtracting them.

Subtraction Rules

Subtraction can be tricky, especially with negative numbers. One essential rule is that subtracting a negative number is equivalent to adding the positive version of that number. For example, in the subtraction problem \(-8 - (-20)\),\(-(-20)\) turns into \(+20\).
Thus, subtraction becomes easier when you convert it into an addition problem, allowing you to add numbers instead of subtracting negatively influenced ones.
To apply this, always think of removing negatives as "adding," thereby simplifying complex subtraction tasks.

Number Line

The number line is a valuable tool to visualize integer operations, like subtraction and addition. It is like a straight road with zero in the center, positive numbers to the right, and negative numbers to the left.
Visualizing \(-8 - (-20)\) on a number line involves first standing on \(-8\). From there, moving \(20\) steps to the right mimics adding \(+20\).
Seeing numbers moved on the line provides a tangible understanding of how subtraction can transform into addition when dealing with negative signs.

Addition

Addition is simply the process of combining numbers to get a total. It becomes crucial when subtracting negative numbers since it transforms subtraction scenarios. For instance, \(-8 + 20\) after converting \(-8 - (-20)\).
Addition here is straightforward: start counting forward from \(-8\) by \(20\) units on the number line.
The result, \(+12\), reflects how addition bridges differences between negative and positive shifts, making these computations more intuitive and manageable.