Problem 12 - Fundamentals of Mathematics

Question

Perform the indicated subtractions. $$ 0-(-16) $$

Step-by-Step Solution

Answer

The result is 16.

Step 1: Understand the Problem

We need to perform the subtraction operation on two numbers: 0 and -16. The operation is given as \(0 - (-16)\).

Step 2: Apply the Rule of Subtraction

Recall that subtracting a negative number is the same as adding the absolute value of that number. Thus, \(0 - (-16)\) becomes \(0 + 16\).

Step 3: Perform the Addition

Now, add the two numbers: \(0 + 16\). This results in \(16\).

Key Concepts

Negative Numbers

Negative numbers are values that are less than zero. When you see a negative sign in front of a number, it indicates that the number is below zero on a number line. Negative numbers have many applications, such as indicating temperatures below freezing or debts in a bank account.

One key aspect to remember about negative numbers is how they interact with other numbers in mathematical operations. For subtraction, like in the exercise where we deal with zero and negative sixteen, understanding the behavior of negative numbers is crucial.

• Negative Sign: Represents numbers below zero.
• On a number line: Move left when the number is negative.
• In subtraction: Treat as adding the opposite (e.g., subtracting -16 becomes adding 16).

Understanding these patterns helps solve problems involving negative values smoothly.

Absolute Value

Absolute value refers to the distance a number is from zero on a number line, regardless of direction. It’s often represented by two vertical bars on either side of the number, like this: |x|. The absolute value of a number is always positive because distance cannot be negative.

For example, the absolute value of -16, written as |-16|, is 16. This measure is crucial when modifying negative operations into positive ones, such as in our subtraction problem: turning subtraction into addition by using the absolute value.

• Absolute Value: Distance from zero.
• Notation: |x| indicates absolute value.
• Always Positive: Represents magnitude without regard to sign.

Knowing how to find and use absolute values effectively allows for easier computation and understanding of number behaviors.

Addition of Integers

Adding integers might seem straightforward, but it's essential to grasp the basics, especially when negative numbers are involved. In integer arithmetic, addition can simplify operations that initially appear as subtractions.

When you "subtract" a negative number as in our exercise (0 - (-16)), you convert the expression into an addition of positive integers: 0 + 16. This change occurs because subtracting a negative essentially cancels out the negatives, making the operation additive.

• Addition of Integers: Combines values on a number line.
• Adding Negatives: Use addition rules effectively (e.g., subtracting negatives).
• Sum: The result when combining integer values.

Once you grasp this, you'll find operations with integers much simpler and intuitive, providing a solid foundation for more complex math challenges.