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Understanding Bar Brackets

Published in Mathematics 3 mins read

How to Solve a Bar Bracket?

Solving a bar bracket, also known as a vinculum, involves following the order of operations, prioritizing the expressions within the bar bracket first.

Bar brackets, or vinculums, are horizontal lines placed above or below an expression, grouping terms together. They function similarly to parentheses, brackets, or braces, indicating a specific order of operations within a mathematical expression.

Solving Bar Brackets: A Step-by-Step Guide

To solve expressions with bar brackets, follow these steps:

  1. Prioritize the inner expressions: Start by simplifying any expressions contained within the bar bracket. This often involves addressing parentheses, brackets, and exponents before performing addition, subtraction, multiplication, and division. Remember the order of operations (often remembered by acronyms like PEMDAS/BODMAS).

  2. Simplify the expression under the bar bracket: Once the inner expressions are simplified, proceed to simplify the entire expression located underneath the bar bracket. This involves performing the operations (addition, subtraction, multiplication, and division) according to the order of operations.

  3. Address expressions outside the bar bracket: Finally, handle any operations or expressions that are outside of the bar bracket.

Example:

Let's say you have the expression: 10 – 4 + (2 x 3) / 2. To solve:

  • We first solve within the parenthesis (2 x 3) = 6 which gives 10 – 4 + 6 / 2.
  • Next, follow order of operations, division before addition/subtraction: 6 / 2 = 3 leading to 10 – 4 + 3.
  • Lastly, perform the addition and subtraction from left to right: 10 – 4 + 3 = 9.

Now consider an example with a bar bracket:

10 − 4 + <u>(2 x 3) / 2</u>

Here, the underlined portion is treated as a single unit. We solve under the bar bracket first following the same steps as above.

  1. Parentheses: (2 x 3) = 6
  2. Division: 6 / 2 = 3
  3. The expression under the vinculum simplifies to 3.

Then the overall expression becomes 10 - 4 + 3 = 9.

Different Types of Brackets

As noted in the YouTube video "BODMAS Question --- Different types of Brackets", various brackets are used in mathematics, including bar brackets, round brackets (parentheses), curly brackets (braces), and square brackets. The order of operations remains consistent; inner brackets are simplified before outer ones.

Conclusion

Remember, the key to solving bar brackets is to work from the inside out, simplifying the grouped expressions step-by-step while adhering to the established order of operations.

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