Problem 16 - Prealgebra

Question

Combine the following by using the rule for addition of positive and negative numbers. $$9+12$$

Step-by-Step Solution

Answer

The sum is 21.

Step 1: Understanding Positive Number Addition

When adding two positive numbers, simply combine them by adding the values together, moving to the right on the number line.

Step 2: Performing the Addition

Add the two positive numbers given in the problem: \(9 + 12\). Calculate it step by step. \(9\) is the first positive number and \(12\) is the second positive number. In this step, just carry out the addition: \(9 + 12 = 21\).

Key Concepts

Positive Numbers

Positive numbers are numbers greater than zero. They're usually the first numbers that we learn about in math. These numbers are used to represent values or quantities that are more than nothing, like having 9 apples or adding 12 more to them. A crucial part of understanding positive numbers is to realize that they're always to the right of zero on a number line. They can be whole numbers, like 1, 2, 3 and so on, or decimal numbers like 0.5, 2.75.

• Example: 9 is a positive number since it's greater than zero.
• 12 is also a positive number because it's more than zero.

When you add two positive numbers together, like in the exercise, you're essentially increasing the total value. This means making the total bigger because you're combining two values that are already above zero. In simpler terms, think of accumulating a larger total in your piggy bank whenever you add more coins.

Number Line

The number line is a visual tool in mathematics that helps us understand the position of numbers in relation to each other. It's like a straight path where numbers are placed at specific intervals. Imagine a ruler, but instead of measuring inches or centimeters, it's marking numbers. Zero is typically in the middle, with positive numbers stretching to the right and negative numbers going to the left.
When adding positive numbers, like 9 and 12, you start at 9 on the number line and move 12 units to the right. This visualization helps in grasping the concept of addition more clearly, showing directly how the values increase.

• The further right you go, the higher the value of the numbers.
• Adding a positive number means moving further to the right.

Prealgebra

Prealgebra is the introductory phase of algebra, and it's all about understanding the basic concepts that will form the foundation for more complex math. It covers fundamental arithmetic operations such as addition, subtraction, multiplication, and division. With prealgebra, you'll begin to see how these operations work together and start to apply them to solve basic equations and problems.

• Focuses on building a strong arithmetic foundation.
• Begins the transition from simple math to algebraic thinking.
• Involves recognizing patterns and understanding how numbers interact.

When you're doing prealgebra, like solving the exercise of adding 9 and 12, you're practicing how these fundamental concepts apply in real-world scenarios. It's about combining numbers to see how they relate, and building the skills to take on more advanced topics later.