Problem 15 - Algebra 1: Concepts and Skills

Question

ADDING REAL NUMBERS Match the exercise with its answer. A. \(-2\) B. 0 C. \(-3\) $$ -1+(-2) $$

Step-by-Step Solution

Answer

The answer is C. -3

Step 1: Identify the Numbers

Identify the numbers to be added which are -1 and -2.

Step 2: Apply Addition of Negatives Rule

When adding two negative numbers, we add their absolute values and make it negative. Therefore, -1 + -2 equals to -3.

Step 3: Match the Result with Provided Options

From the given options A to C, -3 matches with option C. Thus, the answer is C. -3

Key Concepts

Adding Negative Numbers

Adding negative numbers might seem tricky at first, but once you understand the rules, it becomes quite straightforward. When you add two negative numbers together, you want to think of it as combining their absolute values. The result is always a negative number.

Here's how it works:

• Identify the numbers you're dealing with. In this case, it's -1 and -2.
• Find the absolute values of these numbers. The absolute value is simply the number without its negative sign. So, |-1| equals 1 and |-2| equals 2.
• Add these absolute values together: 1 + 2 equals 3.
• Finally, apply a negative sign to this sum, making it -3.

So, -1 + (-2) equals -3 because you "add" their distances from zero and keep the negative sign.

Real Number Operations

Real number operations encompass addition, subtraction, multiplication, and division. These operations follow specific rules that help you solve mathematical problems correctly.

When dealing with addition, especially with real numbers that can be positive or negative, it's essential to use the appropriate rule based on the numbers involved. - When adding two negative numbers, as explained, you sum their absolute values and make the result negative.

In our problem:

• We dealt with two negative numbers: -1 and -2.
• Both have negative signs, so we use the rule for adding negative numbers: add their absolute values and attach a negative sign to the result.

These rules help maintain consistency and accuracy across different mathematical scenarios.

Absolute Value Addition

Absolute value is a crucial concept in mathematics, especially when dealing with real numbers. It's defined as the distance of a number from zero on the number line, regardless of direction.

Understanding absolute value helps simplify many math operations, like addition, because it allows you to work without considering signs temporarily.

Let's consider why this concept is useful in our exercise:

• For the numbers -1 and -2, their absolute values are 1 and 2.
• Adding these absolute values (1 + 2) gives you 3, which is the magnitude of their sum before you apply the sign.

This process underscores why absolute values are foundational—they let you handle magnitudes uniformly before applying direction, ensuring clarity and accuracy.