Problem 12 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

Answer: The result of the subtraction 0 - (-16) is 16.

Step 1: Rewrite the subtraction as an addition

Subtracting a negative number is the same as adding its positive counterpart. Therefore, we rewrite the subtraction as: $$ 0 - (-16) = 0 + 16 $$

Step 2: Perform the addition

Now we perform the addition of the two numbers: $$ 0 + 16 = 16 $$ The result of the subtraction \(0 -(-16)\) is \(16\).

Key Concepts

Understanding Negative Numbers

Negative numbers can sometimes be a bit tricky to understand at first. We use negative numbers to represent a value that is less than zero.

• A negative number is simply the opposite direction on the number line compared to its positive equivalent.
• When you hear the term "negative," think of values like temperatures below zero or debts.

For example, in the exercise provided, the number \(-16\) is a negative number. It is 16 units below zero. This means \(-16\) is the opposite of \(16\). Keeping this concept in mind helps us realize why subtraction with negative numbers often turns into addition. Subtracting a negative number essentially asks us to move in the opposite direction, or towards the positive side.

The Role of Addition in Integer Arithmetic

Addition is a fundamental operation in mathematics and plays a crucial role in integer arithmetic, especially when dealing with negative numbers.

• Adding a positive number is straightforward: you move to the right on the number line.
• However, adding a negative number means moving to the left.

In integer arithmetic, when you subtract a negative number, it actually means you are adding a positive number. This might sound confusing, but remember the exercise example: In the expression \(0 - (-16)\), subtracting \(-16\) is the same as adding \(16\). So, you rewrite it as \(0 + 16\), which equals \(16\). The addition here simplifies the process and ensures that the operation feels less daunting.

Exploring Integer Arithmetic

Integer arithmetic involves operations using whole numbers, both positive and negative. It includes addition, subtraction, multiplication, and division, with unique rules for negative numbers.

• Subtraction transforms when negative numbers are involved: subtracting a negative becomes addition.
• Multiplying and dividing negative numbers follow different rules; for instance, two negatives multiply to make a positive.

Understanding integer arithmetic is pivotal in solving problems like our exercise. When you see subtraction with negative numbers, it's crucial to convert it into addition. This is part of the broader set of rules that govern how integers interact, making arithmetic tasks more intuitive. The key is to remember that negative numbers simply signify direction and change how operations are approached rather than complicating them.