How to Identify Properties in an Equation

Shanefaison
2 min readOct 28, 2023

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As we know that the Commutative Property, Associative Property and Distributive Property are often confusing to identify them for many students. Because they have slight differences, which make them identical to each other. I’ve written some simple ways to identify them in any equation. make sure to read and understand them, put your questions in the comment box for more!

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1. Commutative Property

  • Applies to: Addition and Multiplication
  • Addition: a+b=b+a
  • Multiplication: a×b=b×a
  • Meaning: The order in which two numbers are added or multiplied does not change the result.
  • Example:
  • Addition: 3+4=4+33+4=4+3
  • Multiplication: 5×2=2×55×2=2×5

Students often face problems while dealing with MCQ’s. They often mix up all three with each others and the chances of committing mistake increase.

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2. Associative Property

  • Applies to: Addition and Multiplication
  • Addition: (a+b)+c=a+(b+c)
  • Multiplication: (a×bc=a×(b×c)
  • Meaning: When adding or multiplying several numbers, the way in which the numbers are grouped (or associated) does not affect the final result.
  • Example:
  • Addition: (2+3)+4=2+(3+4)(2+3)+4=2+(3+4)
  • Multiplication: (3×4)×5=3×(4×5)(3×4)×5=3×(4×5)

3. Distributive Property

  • Applies to: Multiplication over Addition/Subtraction
  • Statement: a×(b+c)=a×b+a×c
  • Meaning: Multiplication can be “distributed” across terms inside a parenthesis when the terms are either added or subtracted.
  • Example: 3×(4+2)=3×4+3×23×(4+2)=3×4+3×2

Identifying in Equations

  • To identify these properties in algebraic expressions, look for:
  • Commutative: Change in order of numbers (e.g., a+b=b+a).
  • Associative: Change in grouping of numbers (e.g., (a+b)+c=a+(b+c)).
  • Distributive: Multiplication being applied to each term within a parenthesis (e.g., a(b+c)=ab+ac).

Understanding these properties is crucial in algebra, as they govern the simplification of expressions and the solution of equations. But, if you follow the exact above procedure, your chances of getting confused will be decreased.

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