91Ó°ÊÓ

When we evaluate mathematical expressions, it's crucial to perform operations in the correct order. This order is often remembered by the acronym BIDMAS or BODMAS, standing for Brackets, Indices (or Orders), Division, Multiplication, Addition, and Subtraction. This priority ensures that everyone calculates expressions in the same way and gets the same result.

The first letter, 'B,' stands for brackets, which must be solved first. Following brackets, we tackle indices or orders such as powers and roots. Division and multiplication are next; these operations are of equal priority and should be completed from left to right within the expression. Lastly, addition and subtraction are performed, again moving from left to right.

• **B** - Brackets
• **I/O** - Indices/Orders
• **D** - Division
• **M** - Multiplication
• **A** - Addition
• **S** - Subtraction

In the original exercise, we start by calculating inside the brackets, \(3+2\), before moving onto division, \(10 \div 5\), and finally addressing the addition, \(2+9\).

Mathematical expressions are combinations of numbers, operators, and sometimes variables, structured in a way to represent a particular value or calculation. They can range from simple to complex, depending on the number and types of operations involved. Understanding them is crucial in mathematical problem-solving.

In an expression like \(10 \div(3+2)+9\), numbers are straightforward, and the operators are division and addition. Together they indicate how values interact. The role of brackets is to prioritize operations, grouping parts of the expression so they are calculated first. Learning how to read these expressions accurately helps in executing the correct steps during evaluation.

Sometimes, expressions may include letters (variables) that can represent unknown or variable numbers. However, in the exercise given, we only deal with constants, which simplifies the evaluation process.

Evaluating an expression involves calculating its value by following the order of operations. This process breaks down calculations into simple, manageable steps to ensure accuracy.

Consider our worked example: First, solve inside the brackets to get \(3+2=5\). Then divide 10 by 5 to find its result as 2. Finally, add the already divided number to 9, arriving at the answer 11.

Evaluating expressions is a skill that builds intuitive understanding of mathematics. Practicing with different expressions helps improve problem-solving speed and depth. As you work on expressions, always remember to pause and think about the order required by BIDMAS/BODMAS. This ensures no step is missed or miscalculated.