Problem 20 - Prealgebra

Question

Combine the following by using the rule for addition of positive and negative numbers. $$-7+(-2)$$

Step-by-Step Solution

Answer

The sum is -9.

Step 1: Identify the Terms

In the expression \(-7+(-2)\), we have two terms: \(-7\) and \(-2\). Both of these terms are negative numbers.

Step 2: Apply Addition Rule for Negative Numbers

When adding two negative numbers, we treat them like positive numbers and keep the negative sign. So, we need to add \(7\) and \(2\) as if they are positive: \(7 + 2 = 9\).

Step 3: Assign the Negative Sign

Since both numbers were originally negative, the sum will also be negative. Thus, the final result is \(-9\).

Key Concepts

Integer Addition

Integer addition is simple once you understand the rules. Whether you're adding positive or negative numbers, the process is consistent. When adding integers, it helps to think of a number line.
- Positive integers are numbers that are greater than zero. When you add two positive integers, you are essentially moving right on the number line. - Negative integers are less than zero. When you add two negative integers, you're moving to the left more on the number line.
In general, when dealing with positives and negatives, you can sum the absolute values (ignore the signs, just add the numbers like they are positive) and then apply the sign of the integers you are adding. This process makes solving integer problems much easier.

Negative Numbers

Negative numbers might initially seem tricky, but they are just as straightforward as positive numbers once you get the hang of them. A negative number is any number less than zero, often represented with a minus sign (-) in front.
When adding negative numbers, the key is to remember that you are combining amounts that are below zero. This process is much like owing money; the more money you owe (or negative numbers you add), the greater your debt (the bigger the negative number) becomes.
When you add two negative numbers, the sum will also be negative, because you're adding on to the negative. For example, - both \(-7\) and \(-2\) signal a debt or deficit,- and adding them results in a larger deficit, \(-9\).

Basic Arithmetic

Basic arithmetic forms the foundation of mathematics and is essential for solving problems involving numbers of all kinds. It includes operations such as addition, subtraction, multiplication, and division.
- In the context of addition, you're combining numbers or terms to get a sum. - This is true whether you're dealing with positive or negative numbers. Remember, numbers are tools that help us measure and compute.
When performing basic arithmetic with negative numbers, always pay attention to the signs to guide you through the process. This is especially important during addition: - Negative plus negative results in a more negative value. - Negative plus positive means considering the difference between the numbers. Then, taking the sign of the bigger absolute value.
Grasping these rules will not only aid you in solving problems more efficiently but also build a strong mathematical foundation for more advanced concepts.