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Comparing integers involves deciding which number is larger, smaller, or if they are equal. This concept is foundational in math because it helps us understand relationships between numbers.

When comparing integers, especially negative ones, it is crucial to note that the more to the left a number is on the number line, the smaller it is. For example, -368 is greater than -370 because -368 is to the right of -370 on the number line.

To make comparisons cleaner and more intuitive, it can be helpful to visualize each integer's position on a number line. Remember

• Move left for smaller numbers.
• Move right for larger numbers.

Always take your time to analyze the integers, especially negative values, as they can trick you into thinking something different at first glance.

The absolute value of a number is its distance from zero on the number line, ignoring the direction. It is always a non-negative number.

The absolute value of negative numbers, like -368, is the same as that of their positive counterparts. For example, \(|-368| = 368\), whereas for small numbers or positive ones, the absolute value is simply the number itself, such as \(|2| = 2\). This means that the absolute value function takes any number and turns it into its positive version.

This concept becomes particularly important for distance calculations because it eliminates the direction and focuses on the quantity of separation, making it much easier to compare and understand distances without complicating yourself with negatives.

Discovering the distance between two integers involves calculating how far apart they are on the number line. This can be done using subtraction, followed by taking the absolute value to ensure a positive result.

Consider questions like how far is -368 from -360? Initially, you subtract the two numbers: \(-368 - (-360)\) becomes \(-368 + 360\). This gives a result of \-8\. The final distance is the absolute value of this result, which is 8.

Similarly, to find the distance to -370, you calculate: \(-368 - (-370) = -368 + 370\), resulting in \2\. The absolute value, hence the distance, is \2\.

By always remembering to focus on the absolute value, you ensure that you only measure the actual distance between numbers—no matter their position or negativity on the number line. This clarity is key in solving problems concerning proximity.