Problem 19 - Prealgebra and Introductory Algebra

Question

Add. $$-4+(-5)$$

Step-by-Step Solution

Answer

The sum of -4 and -5 is -9.

Step 1: Understand the problem

The exercise requires to add two negative numbers: -4 and -5. It's crucial to understand that when two negative numbers are added together, the resultant will also be a negative number.

Step 2: Add the absolute values

Next, without considering the negative signs, just add the absolute values of the two numbers. So, the problem turns into adding the numbers 4 and 5 together, which results in 9.

Step 3: Attach the negative sign

Since both numbers were originally negative, the sum of -4 and -5 also needs to be negative. So, add a negative sign to the result from the previous step. Thus, the sum of -4 and -5 is -9.

Key Concepts

Prealgebra

Prealgebra is a critical foundational step in mathematics, serving as a bridge between basic arithmetic and higher-level algebra. A fundamental aspect of prealgebra is understanding how to work with integers, which includes both positive and negative numbers. Grasping the concept of negative numbers and how they interact with each other and with positive numbers through various operations is essential. Developing a strong footing in prealgebra helps students tackle more complex mathematical concepts and problems with confidence.

Negative Number Addition

The addition of negative numbers might initially seem confusing, but it follows a logical set of rules. When adding two negative numbers, you are essentially increasing the amount of 'debt' or 'absence', so the resulting number is more negative. Consider this analogy: If you already owe \(4, and you borrow another \)5, you end up owing $9 in total. In mathematical terms, when adding negative numbers such as \( -4 + (-5) \) the sum retains the negative sign, leading to \( -9 \) as a result. The operation is the addition of their absolute values, followed by attributing a negative sign to the sum.

Mathematical Operations

Mathematical operations, including addition, subtraction, multiplication, and division, are the building blocks for more complex mathematical problem solving. Each of these operations has its own set of rules, especially when dealing with negative numbers. It's pivotal to understand that operations with negative numbers are as logical and consistent as with positive numbers. Applying these operations correctly, such as knowing that 'a negative plus a negative equals a more negative', shows the consistent structure that math is built on. Students need to become familiar with these operations to progress in mathematics.

Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of direction. It is always a non-negative number. For instance, the absolute values of \( -4 \) and \( 4 \) are both \( 4 \) because both points are four units away from zero. When adding negative numbers, such as in our exercise \( -4 + (-5) \) , focusing on the absolute values \( 4 \) and \( 5 \) allows us to disregard the direction of the numbers and simply concentrate on their magnitude. After finding the sum of their absolute values, we then apply the appropriate sign based on the operation's rules.