Problem 88 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ 0-(-8) $$

Step-by-Step Solution

Answer

The result of the operation \( 0 - (-8) \) is 8.

Step 1: Identify the operation

The expression given is \( 0 - (-8) \), which involves subtracting a negative number. When you subtract a negative number, it is the same as adding the positive version of that number.

Step 2: Simplify the expression

Subtracting a negative number from zero turns into an addition. Thus, \( 0 - (-8) \) simplifies to \( 0 + 8 \).

Step 3: Perform the addition

Now, add the numbers: \( 0 + 8 = 8 \).

Key Concepts

Subtracting Negative Numbers

When dealing with the subtraction of negative numbers, it might seem tricky at first. But there's a simple rule you can remember: subtracting a negative number is the same as adding its positive counterpart. In other words, if you see something like

• \( a - (-b) \), it is the same as \( a + b \).

This rule simplifies operations significantly. Let's put this to practice with a small example. If you start with 0 and subtract negative 8, like the equation \( 0 - (-8) \), it will transform into \( 0 + 8 \). Understanding this concept will make your calculations smoother and more intuitive when working with integers.

Addition of Integers

Adding integers, whether they are positive or negative, is foundational in mathematics. Let's delve into how addition works with integers. Imagine integers on a number line:

• Positive integers are to the right of zero.
• Negative integers are to the left of zero.

Consider the addition \( 0 + 8 \). Here, you start at zero on the number line and move eight steps to the right. This equals positive 8. Whenever you add a positive number, you move right; when adding a negative number, you go left. These movements help visualize how the number changes in value.
Also, remember:

• Adding zero to any number does not change its value.
• Integer addition is commutative, which means \( a + b = b + a \).

Simplifying Expressions

Simplifying expressions is about making them as straightforward as possible while keeping the values unchanged. This often involves:

• Combining like terms.
• Reducing complex operations.

Given the simple expression \( 0 - (-8) \), you rewrite it as \( 0 + 8 \) — which is a straightforward simplification.
Let's break it down:

• The expression involved a transformation based on the rule for subtracting negatives, which changed the operation into an addition.
• The final simplified form, \( 0 + 8 \), is easy to evaluate, resulting in 8.

Simplifying expressions helps in solving mathematical problems more efficiently and reduces the potential for mistakes.