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When dealing with fractions, simplifying means reducing the fraction to its simplest form. This involves making the numerator (the top number) and the denominator (the bottom number) as small as possible, while still keeping the same value. For the given problem, you first need to simplify the expression in the numerator before dealing with the fraction itself.

The numerator in this case, "12 - 48," simplifies to "-36," after performing the subtraction. Now, you have a fraction \(-\frac{36}{6}\).

Simplifying this involves dividing both the numerator and the denominator by their greatest common divisor (GCD). Here, since 36 and 6 share a GCD of 6, divide both by 6 to simplify. This results in "-6," which is the simplest form of the fraction.

Understanding integer operations is crucial when working with any arithmetic problems, especially when they involve both positive and negative numbers. In this problem, the operation in the numerator is a subtraction: "12 - 48."

Subtracting integers requires knowing that subtracting a larger number from a smaller one results in a negative number. For example, in this context:

• Subtract 48 from 12, think of it like this: 12 is 48 less than zero, making it -36.

Operations involving integers follow the same basic principles as adding or subtracting positive numbers, but you must keep track of the positive and negative signs to avoid mistakes.

Basic arithmetic involves four main operations: addition, subtraction, multiplication, and division. Understanding and accurately applying these operations form the foundation of solving math problems.

In the exercise provided, the arithmetic steps include subtraction and division. You first subtract 48 from 12 to get -36. This subtraction step requires knowing how to handle negative numbers.

• Negative results occur when the minuend (first number) is smaller than the subtrahend (second number) in subtraction.

After finding the simplified numerator, move on to division. Here, dividing -36 by 6 results in -6. This step involves dividing a negative number by a positive one, which always gives a negative quotient. Remember that if both numbers were negative or positive, the result would be positive.