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Solving Bar Brackets: A Step-by-Step Guide

Published in Mathematics 2 mins read

How to Solve a Bar Bracket?

Solving a bar bracket (also known as a vinculum) in mathematics involves following the order of operations, prioritizing calculations within the bracket before proceeding with operations outside it. This is a fundamental concept in algebra and arithmetic.

  1. Innermost Grouping Symbols First: Bar brackets often contain other grouping symbols like parentheses ( ), square brackets [ ], or curly braces { }. Always begin by simplifying the expressions within the innermost grouping symbols first. This adheres to the principle of working from the inside out.

  2. Simplify Within the Bar Bracket: Once the innermost expressions are simplified, focus on the remaining operations inside the bar bracket. Perform these calculations according to the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

  3. Address Operations Outside the Bar Bracket: After simplifying the expression within the bar bracket, treat the entire result as a single number. Then, proceed with any remaining operations outside the bar bracket, again following the order of operations.

Examples

Let's illustrate with a couple of examples:

Example 1:

Solve: $\overline{3 + 2 \times 4 - 1}$

  1. Inside the bar bracket: We first perform the multiplication: $2 \times 4 = 8$. The expression becomes: $\overline{3 + 8 - 1}$
  2. Continue inside the bar bracket: We now perform the addition and subtraction from left to right: $3 + 8 = 11$, then $11 - 1 = 10$.
  3. Final answer: The solution is 10.

Example 2:

Solve: $\overline{ (2 + 3) \times 5 - 10 \div 2 }$

  1. Innermost parentheses: We begin with $(2 + 3) = 5$. The expression becomes: $\overline{5 \times 5 - 10 \div 2}$
  2. Multiplication and Division (left to right): $5 \times 5 = 25$ and $10 \div 2 = 5$. The expression becomes: $\overline{25 - 5}$
  3. Subtraction: $25 - 5 = 20$.
  4. Final answer: The solution is 20.

Key Considerations

  • Remember the order of operations is crucial for accurate results.
  • Bar brackets are simply another type of grouping symbol, treated the same way as parentheses or square brackets in terms of order of operations.
  • If dealing with nested bar brackets (bar brackets within bar brackets), follow the same principle of working from the innermost bracket outwards.

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