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Name ____________________________________ Date ____________ Period ________ Math Properties Commutative Property of Addition and Multiplication “Sometimes order matters: You do not put on your socks after your shoes. But sometimes order doesn’t matter: You could put on your shoes before your belt” (Math On Call, 1998). Commutative Property of Addition Changing the order of addends does not change the sum. a+b=b+a Ex1) 24 + 16 = 40 and 16 + 24 = 40 24 + 16 = 16 + 24 Ex2) 25 + 147 +75 = 25 + 75 + 147 172 + 75 = 100 + 147 247 = 247 Commutative Property of Multiplication Changing the order of factors does not change the product. axb=bxa 3(4) = 12 4(3) = 12 4(3) = 3(4) Ex1) 5●63●2 = 5●2●63 315●2 = 10●63 630 = 630 Ex2) 6(3)(4) = 4(6)(3) 18(4) = 24(3) 72 = 72 Associative Property of Addition and Multiplication “You associate with friends in groups. The associative properties are all about the ways you can group addends and factors” (Math on Call, 1998) Associative Property of Addition Changing the grouping of addends does not change the sum. (a + b) + c = a + (b + c) NOTE that the order of the addends stays the same, you just group them differently. Ex) (15 +98) + 2 = 15 + (98 +2) 113 + 2 = 15 + 100 115 = 115 Associative Property of Multiplication Changing the grouping of factors does not change the product. (a ● b) ● c = a ● (b ● c) NOTE that the order of the factors stays the same, you just group them differently. Ex) 2 ● (25●4) = (2●25) ● 4 2 ● 100 = 50 ● 4 200 = 200 Zero Property of Multiplication Zero Property of Multiplication Any number multiplied by zero is ZERO. a●0=0 Ex1) 6 ● 0 = 0 Ex2) 0 ● 3 = 0 Identity Properties Identity elements are numbers that combine with other numbers without changing them. The Identity Property of Addition Ex: 5 + 0 = 5 0+5=5 Any number added to Zero is itself. a + 0 = a and 0 + a = a . The Identity Property Multiplication Any number multiplied by one is itself. It is like looking into a mirror Ex: 5 ● 1 = 5 1●5=5 a ● 1 = a and 1 ● a = a Inverse Properties Additive Inverse/ Inverse Property of Addition Any number added to its opposite is zero. a + -a = 0 and 2 + -2 = 0 Multiplicative Inverse/Inverse Property of Multiplication Any number multiplied by its multiplicative inverse (reciprocal) is one 𝟑 𝟒 𝟒 𝟏𝟐 𝟑 𝟏𝟐 · = =𝟏 The Distributive Property When you distribute things, you hand them out. With the distributive property, you can distribute (or hand out) the multiplier to each addend in the group. Remember, no number should feel left out. The Distributive Property You can multiply each term inside a set of parentheses by a factor outside the parentheses. a(b + c) = a●b + a●c Example: 6(3 + 2) = 6●3 + 6●2 18 + 12 a(b – c ) = a●b – a●c Example: 8(x – 4) = 8●x – 8●4 8x - 32