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Subtraction is one of the four basic arithmetic operations, along with addition, multiplication, and division. This operation involves taking one number away from another. The result of a subtraction operation is called the 'difference'. In mathematical terms, if you have two numbers, say 8 and 1, and you want to subtract one from the other, it's written as: \(8 - 1\). In the original exercise, we have to subtract 1 from 8, resulting in 7. Then another subtraction is needed: 7 minus 12. This essential operation helps us determine how much remains when certain quantities are removed.

It's important to note that subtraction can be visualized in various ways such as by using number lines, counters, or even real-world examples like taking apples from a basket.

Parentheses are used in mathematics to group parts of an expression and indicate that the operations within the parentheses should be performed first. This follows the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). For example, in the exercise \((8-1)-12\), we must first calculate the value inside the parentheses.
This results in 7, making the expression 7 - 12. Parentheses ensure that we perform calculations in the correct sequence to get the right answer.

Without parentheses, the meaning of the expression could change completely. Hence, understanding and correctly using parentheses is crucial in solving mathematical problems accurately.

Negative numbers are numbers that are less than zero and are typically represented with a minus sign (−). They can be found on the left side of a number line. In real life, negative numbers can represent various situations like temperatures below zero, owing money, or depths below sea level. In arithmetic operations, working with negative numbers follows specific rules.

For example, in the given problem, we calculated \(7 - 12\) which resulted in \(-5\). This happens because subtracting a larger number from a smaller number results in a negative number. To think about this visually, if you start at 7 on a number line and move 12 spaces to the left, you'll land on -5.
Understanding negative numbers is essential for accurately solving equations and comprehending more advanced math topics.