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Division is a fundamental arithmetic operation that involves splitting a number into equal parts. It is often considered the reverse of multiplication. In mathematical expressions, division is typically represented by the symbol \(\div\) or a slash (\(/\)). Understanding division is crucial because it is frequently the first operation to perform in expressions with multiple arithmetic operations.
In the example given, we have \(10 \div 2\), which simplifies to \(5\). This means that \(10\) is divided into \(2\) equal parts, each with the value \(5\). Before moving on to other operations like subtraction, take the time to fully evaluate and simplify any division present in the expression.

Subtraction is another basic arithmetic operation which involves taking away one quantity from another. It is represented by the minus sign \(-\). Subtraction helps in finding out the difference between numbers.
In our problem, once we had simplified the division to \(5\), the next step was to perform subtraction: \(3 - 5\). This involves taking \(5\) away from \(3\), resulting in \(-2\). Negative results are important in mathematics, as they indicate a value is less than zero.

The order of operations is a set of rules that dictate the sequence in which calculations should be performed to avoid ambiguity. This is crucial in mathematics when an expression includes more than one type of operation. The standard order of operations can be remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the provided exercise, the order of operations required performing the division \(10 \div 2\) before executing the subtraction \(3 - 5\). Strict adherence to this order ensures the correct solution, which in this case is \(-2\). Always perform operations from left to right for division and multiplication, as well as for addition and subtraction, unless parentheses suggest another arrangement.