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The commutative property is important because it doesn't work with all operations. Addition and multiplication have commutative properties, but subtraction and division don't. We know 5+4 is the same as 4+5, but 5-4 = 1 while 4-5= -1. With subtraction, order matters! Watch this video for examples of how to apply these laws in arithmetic to make mental math easier.
Source: Khan Academy, https://www.khanacademy.org/math/in-in-class-6th-math-cbse/x06b5af6950647cd2:whole-numbers/x06b5af6950647cd2:commutative-property/v/commutative-law-of-addition This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.