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When simplifying mathematical expressions, the BIDMAS/BODMAS rule is a crucial guideline. The acronym stands for:

• Brackets
• Indices (or Orders)
• Division and Multiplication
• Addition and Subtraction

This rule helps us remember the order in which operations should be performed to avoid mistakes and obtain the correct result.
In our original exercise, the expression "5+[2+(-5)]+(-2)" uses brackets to prioritize certain operations. According to BIDMAS/BODMAS, we handle the operations inside the brackets first. So, before addressing any additions or subtractions, we simplify "2 + (-5)". Once inside the bracket is simplified, we move on to the rest of the expression following the rule.

Negative numbers can often be a source of confusion, but they're easy to manage once you understand them.
A negative number is simply a number less than zero, often represented with a minus sign (-). When handling negative numbers in expressions, recognizing how they interact with other numbers is key.
For example, in the expression "2 + (-5)", you substitute this as "2 - 5", resulting in "-3".
Handling multiple negatives together can also be tricky. Two negative signs right next to each other can behave like a positive, but when they're separate, they contribute to making the number smaller, as shown in the exercise where "+(-2)" became "-2".
Always take care to distinguish between subtraction signs and negative number signs when simplifying.

The order of operations is the sequence in which mathematical operations should be performed to ensure that calculations are carried out correctly. This sequence aligns closely with the BIDMAS/BODMAS rule.
After simplifying any expressions within brackets, the next step is to handle indices or exponents. Follow this with multiplication and division, which are prioritized over addition and subtraction. However, a common mistake is to think multiplication always comes before division, and addition always comes before subtraction. Instead, perform these operations as they appear from left to right.
In the expression "5 + [-3] + (-2)", once the brackets are simplified, the next step is straightforward subtraction, performed from left to right:

• "5 - 3" results in "2"
• Then "2 - 2" results in "0"

Adhering closely to the order of operations helps ensure accurate results in our math calculations.