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Published byAliza Toone Modified about 1 year ago

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SOL 7.16

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Addend: a number that is added to another Factor: a number that is being multiplied Sum: The answer to an addition problem Product: The answer to a multiplication problem Difference: The answer to a subtraction problem Reciprocal: the multiplicative inverse of a number Make sure to learn these important terms…we will use them from now on! Identity Element: numbers that combine with other numbers without changing the other numbers Inverse: numbers that combine with other numbers and result in identity elements

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Addition Multiplication Changing the order of the addends does not change the sum. Changing the order of the factors does not change the product. For Example:

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What Changed from one side of the equal sign to the other? What should we look for to help us identify this property? The order of the addends or factors changed. I think of commuters when I think of the commutative property. You start one way and end, but to start again you must leave where you are and go back to where you started. Complete the examples using the commutative property. a) = b) 8 (3 - 2) = c) 6- ( 5+ 9) = d) fg= (3 - 2)8 6-(9 + 5) gf Write down what you think of!

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Addition Multiplication Regrouping the addends does not change the sum. Regrouping the factors does not change the product. For Example:

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What Changed from one side of the equal sign to the other? How is the associative property different from the commutative? The number inside of the grouping symbols or parentheses changed. In the commutative property the order of the numbers changed, but the numbers that were in the parentheses changed with the associative. Complete the examples using the associative property. a) 2+(4 + 5) = b) 8(3 2) = c) 6+( 5+ 9) = d) a(bc) = (2 + 4) + 5 (8 3) 2 (6+5) + 9 (ab)c How will you remember this property?

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Subtraction? Division? Is subtraction commutative? Associative? Is division commutative? Associative? For Example:

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The product of a number and the sum (or difference) of two other numbers equals the sum (or difference) of the products of the number and each other number. For Example:

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What Changed from one side of the equal sign to the other? What should we look for to help us identify this property? The number on the outside of the parentheses was passed out to the numbers inside the parentheses. I think of distributing flyers to the class. You start with one stack of flyers, then once you distribute the stack to the class each person has that same flyer. Complete the examples using the distributive property. a) 2(4 + 5) = b) 8 (3 - 2) = c) 6( 5+ 9) = d) e(f-g)= (24) + (25) (8 3)- (82) (65) + (69) (ef) – (eg) Write down what you think of!

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Identity Inverse The sum of any real number and zero is equal to the given real number. The sum of a number and its additive inverse (opposite) always equals zero. For Example:

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Identity Inverse The product of any real number and one is equal to that given number. The product of a number and its multiplicative inverse (reciprocal) always equals one. For Example:

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What are the identity elements? How can we tell the identity properties from the inverse properties? The additive identity element is 0 and the multiplicative identity element is one. The identity properties result in the same real number that was in the problem. Also, in the identity properties 0 and 1 are being added or multiplied. They are the answers in the inverse properties! Complete the examples using the identity properties. a) = b) 8 (1) = c) 0+( 5+ 9) = 4 8 (5+9)

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Is there a number with no additive inverse? What is the difference between the additive inverse and the multiplicative inverse? Zero does not have an opposite. It is neither positive or negative to have an additive inverse. With the additive inverse you are adding the opposite, but with multiplicative inverse you are multiplying the reciprocal, not the opposite. Complete the examples using the inverse properties. -4 2

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The product of any real number and zero is zero! For Example:

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Both the Multiplicative Property of Zero and the Additive Identity both have an answer of zero. How will you remember which property is which? The multiplicative property of zero has a product of zero and there is a zero both on the right and the left of the equal sign. The additive identity has a sum of zero and there is only a zero on one side of the equal sign. Complete the examples using the multiplicative property of zero. a) 2(0) = b) 0 = 0 c)( 5- 9) ___ = 0 0 any real number 0

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Let’s see if you can identify these properties!

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