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Negative numbers are numbers less than zero. They are very important in mathematics as they allow us to represent values that are below a defined baseline, often zero in many contexts. Consider the case of a bank account; a positive balance indicates you have money, while a negative balance means you owe money. So negative numbers help to show deficits or losses in many real-life situations.
In mathematical terms, negative numbers are typically written with a minus sign (-) in front of them. For example, -3 represents a negative three. When you're dealing with negative numbers, always remember that on a number line, negative numbers are located to the left of zero.
This exercise of finding the difference 137 - 355 resulted in -218 because the larger number was subtracted from the smaller one, bringing us into the realm of negative numbers. Understanding the interaction of negative numbers with positive ones is crucial in arithmetic.

Arithmetic operations are the basic operations in mathematics. They include addition, subtraction, multiplication, and division. These operations are the foundation of most mathematical calculations and are used regularly in daily life.
1. **Addition (+):** Combining numbers into a larger number. 2. **Subtraction (-):** Taking one number away from another. 3. **Multiplication (×):** Repeated addition of a number. 4. **Division (÷):** Splitting a number into equal parts. Understanding how these operations interact, especially with negative numbers, is fundamental. In subtraction, when taking a larger number away from a smaller one, as shown in this exercise, we involve negative numbers. This is because you're moving into values below zero on the number line. Consistently practicing these operations with different kinds of numbers helps in solidifying arithmetic skills.

Integer subtraction involves taking one integer from another. It's crucial to understand that integers include negative numbers, zero, and positive numbers. When performing subtraction with integers, particularly when the minuend (first number) is smaller than the subtrahend (second number), the result becomes negative.
For example in our original problem, subtracting 355 from 137 gave us -218. This showcases two essential points to remember in integer subtraction: - **Order matters:** Always subtract the second integer from the first. The sequence affects the result entirely. - **Positive to negative:** If the integer you're subtracting is greater than the starting integer, the result will be negative.
With practice, navigating through integer subtraction and understanding when and why results turn negative becomes intuitive.