91Ó°ÊÓ

Understanding absolute value is important when adding integers because it gives the number's size without considering its sign. Simply put, the absolute value is always a non-negative number. For example, the absolute value of

• \(-18\) is \(18\)
• \(+49\) is \(49\)

Both of these absolute values tell us how far the numbers are from zero on a number line, regardless of direction.
When you're adding numbers with different signs, like \[-18 + 49\], focusing on absolute values helps us decide what arithmetic operation to perform. In this case, since one number is negative and the other is positive, we can subtract the smaller absolute value from the larger one.

In the context of adding integers like \[-18 + 49\], arithmetic operations are the steps needed to combine the numbers correctly. Here, you initially ignore the signs and perform subtraction of absolute values because one number is negative and the other is positive.
Remember this simple rule:

• When adding numbers with the same sign, add their absolute values and keep the sign.
• When adding numbers with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.

For the example, you would calculate \[49 - 18 = 31\], then determine the sign of the result based on the larger absolute value's original sign.

Positive and negative numbers follow simple yet crucial rules that dictate how they behave in arithmetic operations, especially addition.

Positive numbers are usually larger than zero (e.g., 1, 2, 3, ...), and negative numbers are smaller than zero (e.g., -1, -2, -3, ...). When you encounter an operation like \[-18 + 49\], you see one negative and one positive number.
This situation leads us back to the rule: when adding numbers with different signs, subtract their absolute values. Since \(+49\) has a larger absolute value than \(-18\), the result, in absolute terms, will be positive.

• Keep the sign of the number with the larger absolute value.
• In this case, \[18\] has a smaller absolute value compared to \[49\], so the overall sum is positive, resulting in\[+31\].

Fully understanding these rules allows for quick and accurate calculations in a wide variety of math problems.