Problem 49 - Prealgebra and Introductory Algebra

Question

Find the total of \(-3,-8,\) and 12

Step-by-Step Solution

Answer

The sum of -3, -8, and 12 is 1.

Step 1: Sum up the negative numbers

First, add up the negative numbers which are -3 and -8. This gives a sum of -11.

Step 2: Sum up the total with the positive number

Next, add up the result from Step 1 which is -11 with the positive number 12. This gives a final sum of 1.

Key Concepts

Negative Numbers

Negative numbers are a fundamental concept in math and are found on the left side of the number line. They are less than zero, such as

• -1
• -5
• -100

Negative numbers are characterized by the minus sign "-" before them. They represent a value of less or a loss.
For example, if you have \(-3\), it means three less than zero, similar to owing money to someone.
When adding negative numbers, imagine combining all the things you owe.
This exercise requires you to first add the two negative numbers together.
For instance, adding \(-3\) and \(-8\) would be treated like a more extensive debt, resulting in \(-11\).
Visualizing a number line can be extremely helpful. Moving left for each negative number can simplify understanding.

Positive Numbers

Positive numbers are pretty straightforward. They are greater than zero and located to the right on the number line,

• +2
• +10
• +57

These numbers don't have a sign in front of them, indicating they are positive unless explicitly needed.
When dealing with positive numbers, think of gaining or adding value, like increasing money in your piggy bank.
In the exercise, \(12\) is the positive number you need to add to the result of the negative numbers sum.
By adding \(-11\) and \(12\), you move forward 12 units from \(-11\) on the number line, which leaves you at \(1\).
Understanding positive and negative numbers' interaction is crucial for solving such equations.

Prealgebra Methods

Prealgebra builds the foundation for understanding algebra. It's about learning the basic rules and operations that govern mathematical equations.
In this problem, skills in addition are key — knowing how negative and positive numbers interact.

• Combing negative numbers initially: Treat them as owing more when added.
• Adding a positive number after negatives: Think of getting some relief from debt.

The step-by-step solution provided demonstrates these ideas clearly: 1. Sum the negatives to get their total value. 2. Add the sum to the positive number to reach the final result.
This exercise exemplifies a prealgebra approach, reinforcing the concepts of integer addition by breaking down problems into simpler, more manageable steps.
Building these skills will support more advanced math topics in the future.