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## Properties 0f Real Numbers

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**Properties 0f**Real Numbers I can’t wait until we learn about fake numbers!**Properties 0f Real Numbers**The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.**Commutative Property of Addition**a + b = b + a Example: 7 + 3 = 3 + 7 Two real numbers can be added in either order to achieve the same sum. Does this work with subtraction? Why or why not?**Commutative Property of Multiplication**a x b = b x a Example: 3 x 7 = 7 x 3 Two real numbers can be multiplied in either order to achieve the same product. Does this work with division? Why or why not?**Associative Property of Addition**(a + b) + c = a + (b + c) Example: (29 + 13) + 7 = 29 + (13 + 7) When three real numbers are added, it makes no difference which are added first. Notice how adding the 13 + 7 first makes completing the problem easier mentally.**Associative Property of Multiplication**(a xb) xc = a x (b xc) Example:(6 x 4) x 5 = 6 x (4 x 5) When three real numbers are multiplied, it makes no difference which are multiplied first. Notice how multiplying the 4 and 5 first makes completing the problem easier.**Additive Identity Property**a + 0 = a Example: 9 + 0 = 9 The sum of zero and a real number equals the number itself. Memory note: When you add zero to a number, that number will always keep its identity.**Multiplicative Identity Property**ax 1= a Example:8x1 = 8 The product of one and a number equals the number itself. Memory note: When you multiply any number by one, that number will keep its identity.**Properties 0f Real Numbers**TIME OUT!!! My brain’s about to explode with all of this crazy property stuff! What’s wrong? Hang in there, Sparky! We only have a few more.**Distributive Property**a(b + c) = ab + acora(b – c) = ab – ac Example:2(3 + 4) = (2x 3) + (2x 4) or 2(3 - 4) = (2x 3) - (2x 4) Distributive Property is the sum or difference of two expanded products.**Additive Inverse Property**a + (-a) = 0 Example: 3 + (-3) = 0 The sum of a real number and its opposite is zero.**You are now ONE with the properties of real numbers.**Sparky’s fixin’ to become one with a triple decker, chili- fire bean burrito! Go forth and use them wisely! Use them confidently! And use them well, my friends! My job here is done!