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How do you simplify in pre algebra?

Published in Pre-Algebra Simplification 3 mins read

Simplifying in pre-algebra involves reducing expressions to their most basic form by combining like terms and performing operations. The goal is to make the expression easier to understand and work with.

Understanding Simplification

Simplification in pre-algebra generally means rewriting an expression in a more compact and manageable form. This often involves:

  • Combining like terms
  • Applying the distributive property
  • Performing arithmetic operations (addition, subtraction, multiplication, division)

Key Techniques for Simplifying Expressions

Here are the fundamental techniques to simplify expressions in pre-algebra:

1. Combining Like Terms

  • Definition: Like terms are terms that have the same variable raised to the same power.

  • Process: Combine like terms by adding or subtracting their coefficients.

    Example:

    3x + 5x can be simplified to 8x because 3x and 5x are like terms.
    7y - 2y + 4 simplifies to 5y + 4. The 7y and -2y are like terms and can be combined.

2. Applying the Distributive Property

  • Definition: The distributive property states that a(b + c) = ab + ac.

  • Process: Multiply the term outside the parentheses by each term inside the parentheses.

    Example:

    2(x + 3) simplifies to 2x + 6.

    -3(2y - 5) simplifies to -6y + 15.

3. Order of Operations (PEMDAS/BODMAS)

  • PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • BODMAS: Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
  • Process: Follow the order of operations to perform calculations correctly.

4. Simplifying to Zero

As mentioned in the reference, sometimes an expression simplifies to zero. "Then you can just say that it's zero. If you have to write a zero okay. We don't always have to write a zero for an answer. Sometimes."

Example:
5x - 5x = 0

Examples of Simplification

Here are a few examples demonstrating how to simplify expressions:

  • Example 1: 4x + 2y - x + 3y

    1. Combine like terms: (4x - x) + (2y + 3y)
    2. Simplify: 3x + 5y

  • Example 2: 3(a + 2b) - b

    1. Apply the distributive property: 3a + 6b - b
    2. Combine like terms: 3a + 5b

  • Example 3: 2(x - 1) + 5

    1. Apply the distributive property: 2x - 2 + 5
    2. Combine like terms: 2x + 3

By mastering these techniques, you can effectively simplify expressions in pre-algebra, making them easier to solve and understand.

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