How Do You Do Brackets?

To "do" brackets in mathematics means to perform the operations enclosed within them first, following the order of operations. This ensures expressions are evaluated consistently to arrive at the correct answer.

Understanding Brackets in Math

Brackets, also known as square brackets [ ], are grouping symbols used in mathematical expressions. They serve a similar purpose to parentheses ( ) but are often used when multiple levels of grouping are needed.

The primary rule when encountering brackets is to evaluate the expression inside the brackets before performing any operations outside of them. This rule is a fundamental part of the order of operations, commonly remembered by acronyms like PEMDAS or BODMAS.

• Parentheses / Brackets
• Exponents / Orders
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

According to this order, calculations within grouping symbols (like brackets and parentheses) are always performed first.

How to Evaluate Expressions with Brackets

When you see brackets in a problem, follow these steps:

1. Locate the innermost set of brackets or parentheses.
2. Perform all calculations inside this set of grouping symbols, following the standard order of operations (exponents, then multiplication/division, then addition/subtraction).
3. Replace the bracketed expression with the single value you calculated.
4. Repeat steps 1-3 until all grouping symbols have been removed.
5. Continue evaluating the rest of the expression outside the removed brackets, following the order of operations.

For example, in a problem that might involve brackets, you would work through the steps inside the brackets. As seen in the reference provided, a calculation like 16 minus 5 which equals 11 would be performed as a step within solving a larger problem. This demonstrates evaluating an expression (16 - 5) that might be contained within brackets, leading to the result 11. The reference notes that "all of these problems will be worked the same way," emphasizing the consistent application of rules like prioritizing operations within brackets.

Example

Let's look at an example:

Evaluate: 5 + 2 * [3 + (16 - 5) / 11]

1. Start with the innermost grouping: (16 - 5)
   • 16 - 5 = 11
   • Expression becomes: 5 + 2 * [3 + 11 / 11]
2. Now work inside the square brackets [ ]. Follow the order of operations within the brackets: Division before Addition.
   • 11 / 11 = 1
   • Expression inside brackets is now 3 + 1
   • 3 + 1 = 4
   • Expression becomes: 5 + 2 * [4] (or simply 5 + 2 * 4)
3. Now evaluate the remaining expression outside the brackets. Follow the order of operations: Multiplication before Addition.
   • 2 * 4 = 8
   • Expression becomes: 5 + 8
4. Perform the final addition.
   • 5 + 8 = 13

The final answer is 13. By "doing" the brackets first, we correctly evaluated the expression.

In summary, doing brackets means prioritizing and completing the mathematical operations contained within them before proceeding with the rest of the expression.