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Apply the commutative property

The commutative property establishes that changing the order of addends or factors does not change the sum or product: a+b=b+aa+b=b+a and a×b=b×aa\times b=b\times a for whole numbers. It supports efficient mental calculation and recognizing equivalent expressions, while distinguishing operations for which the property does not hold, such as subtraction and division; this scope does not extend to more abstract algebraic structures.

Detailed Explanation: Apply the commutative property

The commutative property means you can change the order of numbers in addition or multiplication without changing the answer.

  • Addition: a+b=b+aa+b=b+a
  • Multiplication: a×b=b×aa\times b=b\times a

Example: Find 4×254\times 25.

  1. Switch the order of the factors:
4×25=25×44\times 25=25\times 4
  1. Multiply:
25×4=10025\times 4=100

So,

4×25=1004\times 25=100

Changing the order can make a problem easier to solve mentally. Remember, this property works for addition and multiplication, but not generally for subtraction or division.

Learn by doing: Apply the commutative property

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Multiplication - Commutative Property


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