91Ó°ÊÓ

Integer addition is a core concept you'll use often in mathematics. Integers include whole numbers and their opposites, such as -4 and 10. When adding integers, it's important to consider their signs.

• When adding two positive integers, the result is positive (e.g., 3 + 5 = 8).
• When adding two negative integers, the result is negative (e.g., -2 + -3 = -5).
• When adding a positive integer and a negative integer, the result depends on which number is bigger in absolute value.

In our example, we are adding -4 and 10. Here, 10 is positive and -4 is negative. To find the sum, subtract the smaller absolute value (|-4| = 4) from the larger absolute value (|10| = 10), which gives us 6. Since 10 is greater in absolute value and is positive, the final answer is 6.

A number line is a helpful visual tool for understanding how to add and subtract integers. It allows you to easily see the movement between numbers.

To use a number line:

• Draw a horizontal line and mark equal intervals to represent the integers.
• Place 0 in the center. Positive numbers are placed to the right of 0, while negative numbers are to the left.

Let's apply it to our example, -4 + 10. Begin at -4 on the number line. Because we are adding 10, move 10 units to the right. Each step to the right increases the value by 1. When you move 10 steps from -4, you end up at 6 on the number line. This movement clearly illustrates that -4 + 10 = 6.

Understanding arithmetic operations like addition, subtraction, multiplication, and division is essential in algebra and beyond. Let's focus on addition since that's our current operation.

Arithmetic addition follows a few basic rules:

• Positive + Positive = Positive
• Negative + Negative = Negative
• Positive + Negative or Negative + Positive depends on the absolute values

When adding a positive number to a negative number, think of the number line. Moving rightwards (positive direction) or leftwards (negative direction) helps visualize how these numbers interact. In the example -4 + 10, we're effectively combining these movements. The higher positive value (10) outweighs the smaller negative value (4), resulting in a positive sum of 6. This balance and movement are critical for understanding more complex algebraic expressions.