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Properties of Operations with Real Numbers 1Associative Property of AdditionAssociative Property of Addition is when the parenthesis changes in a group of numbers. Even though the parenthesis changes the problem is still the same.For example: (a+b)+c = a+(b+c)With Numbers: (1+2)+3 = 1+(2+3)Or: 6+(12+18) = (6+12)+18Or: (22-222)+2222 = 22-(222+2222)With pictures:

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2Associative Property of MultiplicationAssociative property of multiplication is when the parenthesis change in a problem. Just like the associative property of addition.For example: (ab)e = a(be)With numbers: (5x3)x2=5x(3x2)Or: (3x6)x9=3x(6x9)Or: 222x(40x5)=(222x40)x5With pictures:

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3Commutative Property of AdditionThe commutative property of addition is when order doesnt matter. As long as you have the same numbers order doesnt matter.For example: a+b+c = b+c+aWith numbers: 5+6+8 = 6+8+5Or: 20+55+33 = 55+20+33Or: 232+111+445 = 111+445+232With pictures:

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++4Commutative Property of MultiplicationThe commutative property of multiplication is when order doesnt matter. Just like the commutative property of addition as long as the numbers stay the same order doesnt matter.For example: df = fdWith Numbers: 2 x 3 = 3 x 2Or: 11 x 16 x 6 = 6 x 11 x 16Or: 321 x 400 x 9 = 9 x 400 x 321With pictures:

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5Distributive PropertyThe distributive property is when you share whats outside of the parenthesis with whats on the inside. This is called distributing. Usually when you distribute you are using multiplication.For example: b(c+f) = bc+bfWith numbers: 5(2+6) = 5x2 + 5x6Or: 22(11+14) = 22x11 + 22x14Or: 453(221+112) = 453x221 + 453x112With pictures:

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6Identity Property of AdditionWhen using the Identity property of addition you will always get the original number you started with. Always.For example: b+0=bWith numbers: 4+0=4Or: 16+0=16Or: 636+0=636With pictures:+=

7Identity Property of MultiplicationIn the identity property of multiplication you will always get the original number. But unlike identity property of addition you usually multiply by one.For example: M(1) = MWith numbers: 6x1=6Or: 25x1=25Or: 589x1=589With pictures:

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8Multiplicative property of ZeroWhen using the multiplicative property of zero your answer is always zero. Never changes.For example:M(0)=0With numbers: 50 = 0Or: 750 = 0Or: 25030 = 0With pictures:

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9Additive inverse propertyWhen using the additive inverse property the answer is always zero. Its usually a positive and a negative number. Even when it doesnt have the parenthesis, and the answer is still zero, it is the additive inverse property. Just like the multiplicative property of zero.For example: c + (-c) = 0With numbers: 6+(-6) = 0Or: -26+26=0Or: 244-244=0 With pictures:+

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-010Multiplicative Inverse PropertyWhen using the multiplicative inverse property your answer is one. Usually you are multiplying by the reciprocal.For example:a 1 aWith numbers: 6 1 1 6Or: 25 1 1 25 Or: 345 1 1 345With pictures:

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11Reflexive PropertyAny quantity is equal to itself. That means any number is equal to itself.For example: ccWith numbers: 66Or: 5555Or: 124124With pictures:

12Symmetric PropertyIf one quantity equals another, then the second quality equals the first.These are usually if/them statements.For example: If bc then cbWith numbers: If 224 then 422Or: If 161632 then 321616Or: If 111222333 then 333222111With pictures:

13Transitive PropertyDuring the transitive property a first amount equals a second amount, and a second amount equals a third amount then the first amount equals the third. Usually an if then statement, and has three parts.For example: If mn and na then maWith numbers: If 112 and 022 then 1102Or: If 121224 and 12224 then 1212122Or: If 5454108 and 912108 then 5454912With pictures:

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