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What is the order of operations in 8th grade math?

Published in Order of Operations 3 mins read

The order of operations in 8th grade math, and generally, is a set of rules that dictate the sequence in which mathematical operations are performed to ensure consistent and correct results. This order is often remembered using the acronym PEMDAS.

Understanding PEMDAS

PEMDAS outlines the following order:

  1. Parentheses: Operations inside parentheses (or other grouping symbols like brackets or braces) are always performed first.
  2. Exponents: Next, calculate any exponents or powers.
  3. Multiplication and Division: Multiplication and division are performed from left to right as they appear in the expression.
  4. Addition and Subtraction: Finally, addition and subtraction are performed from left to right as they appear in the expression.

This means you must handle parentheses first, then exponents, followed by multiplication and division (working left to right), and lastly, addition and subtraction (also working left to right).

Detailed Breakdown

Here's a more detailed look at each step:

  • Parentheses/Grouping Symbols: This includes any type of grouping, such as (), [], and {}. Operations within these symbols are always the first priority. For nested parentheses, work from the innermost set outwards.
  • Exponents: After parentheses, calculate any exponential expressions. This involves raising a base number to a power.
  • Multiplication and Division: These are performed from left to right as they appear. There isn't a strict order between multiplication and division; you resolve them sequentially from left to right.
  • Addition and Subtraction: Similar to multiplication and division, addition and subtraction are also done from left to right as they appear in the expression.

Example

Let's analyze the example from the provided reference:

3 x 8 + 18 / 2

Following PEMDAS:

  1. There are no parentheses or exponents.
  2. Perform multiplication and division from left to right:
    • 3 x 8 = 24
    • 18 / 2 = 9
  3. Now the expression becomes: 24 + 9
  4. Perform the addition: 24 + 9 = 33

Therefore, the correct answer to 3 x 8 + 18 / 2 is 33.

Practical Implications

Understanding the order of operations is crucial for:

  • Correctly evaluating mathematical expressions.
  • Avoiding errors in calculations.
  • Ensuring consistent results, especially when dealing with more complex equations.

By adhering to the PEMDAS order, students can accurately solve mathematical problems and build a strong foundation for more advanced mathematical concepts. As stated by Sal from Khan Academy, "every single equation that you do will go in this order: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction."

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