Problem 17 - Fundamentals of Mathematics

Question

Find the sums. $$ -8+0 $$

Step-by-Step Solution

Answer

The sum of -8 and 0 is -8.

Step 1: Analyze the Problem

We are asked to find the sum of two numbers: -8 and 0. This involves basic arithmetic addition.

Step 2: Apply the Rule of Adding Zero

The rule of adding zero states that any number plus zero equals the number itself. Therefore, we apply this rule to the problem: \(-8 + 0 = -8\)

Step 3: Write the Final Answer

Based on the application of the rule in the previous step, the final sum is:\(-8\)

Key Concepts

Adding Zero Rule

In arithmetic, the 'adding zero rule' is a straightforward yet important concept. It states that when you add zero to any number, the number retains its original value. You can think of zero as the neutral number in addition. It doesn't change the number it is added to.

For example:

• 5 + 0 = 5
• -3 + 0 = -3

This rule is useful because it simplifies calculations and can confirm the stability of a number in equations. Remember, zero is like adding nothing to the equation. So, when \(-8 + 0 = -8\), it follows this same rule, leaving -8 unchanged.

Negative Numbers

Negative numbers are numbers that are less than zero and are represented with a minus sign (-). They appear on the left side of the number line. Understanding negative numbers is crucial in many areas of mathematics, including arithmetic, algebra, and beyond.

Here are some key points about negative numbers:

• They are the opposite of positive numbers.
• When added to their positive counterpart, they neutralize each other: e.g., -4 + 4 = 0.
• Adding a negative number is like subtracting: e.g., 5 - 2 is the same as 5 + (-2) = 3.

In the exercise, the number -8 is negative, which indicates that it is 8 units to the left of zero on the number line. When we add zero, negative 8 doesn't move, it just stays as it is.

Addition Problems

Addition problems involve combining two or more numbers to find their total or sum. There are several strategies for solving addition problems, depending on the complexity of the numbers involved.

Basic addition problems, like adding zero or combining small numbers, can often be solved quickly in one's head. For larger numbers or those that involve carrying over (like 112 + 238), it might be helpful to write them down or use a calculator.

Here are some tips for solving addition problems:

• Identify the numbers being added.
• Look for simple addition rules, such as the adding zero rule.
• Write down steps if the problem feels complex.
• Double-check your calculation to make sure.

In the given exercise, the problem is simple due to the adding zero rule. Therefore, \(-8 + 0 = -8\), a straightforward computation.