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How do you use BODMAS in algebra?

Published in Algebra Operations 3 mins read

BODMAS, or the order of operations, is crucial in algebra to ensure you evaluate expressions correctly. It dictates the sequence in which you perform mathematical operations. Here's how BODMAS applies in algebra:

Understanding BODMAS

BODMAS stands for:

  • Brackets
  • Orders (powers and square roots)
  • Division
  • Multiplication
  • Addition
  • Subtraction

According to the provided reference [BODMAS with Algebra - YouTube], "The thing you need to worry about is powers. So squaring cubing square rooting that would all take place here. Then you get your division multiplication. And your addition and subtraction." This clarifies that powers (orders) are addressed before division and multiplication, which are then followed by addition and subtraction.

Applying BODMAS in Algebraic Expressions

When dealing with algebraic expressions, it's essential to follow the BODMAS order to correctly simplify or evaluate the expression. Here’s a step-by-step breakdown:

  1. Brackets:

    • First, evaluate any expressions inside brackets or parentheses.
    • Start from the innermost brackets and work your way outwards.
    • Example: In the expression 2(x + 3) + 5, you would first handle the (x + 3) portion if x has a value, or handle its expansion if you are simplifying the expression.

  2. Orders:

    • Next, address powers, roots, or indices.
    • This includes squaring, cubing, square rooting, and other similar operations.
    • Example: In 3y² + 4, you must perform the squaring operation y² before any multiplication or addition.

  3. Division and Multiplication:

    • Perform division and multiplication from left to right in the order they appear.
    • These operations have the same precedence, so you work through them from left to right.
    • Example: In 10 ÷ 2 × a, you divide 10 by 2 first, then multiply by a.

  4. Addition and Subtraction:

    • Finally, perform addition and subtraction from left to right in the order they appear.
    • Like division and multiplication, addition and subtraction have equal precedence.
    • Example: In p + 7 - 2, you first add p + 7, then subtract 2.

Practical Insights and Examples

Here are some practical examples to illustrate how BODMAS is used in algebra:

  • Example 1: Simplify 2(x + 4)² - 7

    1. Brackets: Start by addressing the expression inside brackets: (x + 4) - although we don't know what x is, the expansion still needs to be handled.
    2. Orders: Square the bracket: (x+4)² will expand to x² + 8x + 16.
    3. Multiplication: Multiply by 2: 2(x² + 8x + 16) = 2x² + 16x + 32.
    4. Subtraction: Subtract 7: 2x² + 16x + 32 - 7 = 2x² + 16x + 25.

  • Example 2: Evaluate (3a + 6) / 3, when a = 5

    1. Brackets: Calculate the expression inside the brackets: 3 * 5 + 6 = 15 + 6 = 21
    2. Division: Divide by 3: 21 / 3 = 7

  • Example 3: Solve 2(x + 3) / 4 - 5, when x = 10

    1. Brackets: Calculate inside the brackets 10 + 3 = 13
    2. Multiplication: Multiply by 2: 2 * 13 = 26
    3. Division: Divide by 4: 26/4 = 6.5
    4. Subtraction: Subtract 5: 6.5 - 5 = 1.5

Key Takeaways

  • Always follow BODMAS strictly.
  • Work from left to right for operations of the same precedence (division and multiplication, and addition and subtraction).
  • Be careful when simplifying or evaluating algebraic expressions – a simple misstep can lead to an incorrect answer.
  • Understanding BODMAS is critical for consistent and accurate results when solving equations, simplifying expressions, and solving for variables in algebra.

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