Properties of Operations
Do Now: Do you think that the order in which we add or multiply numbers matters? For example, does it matter whether we do 4 + 6 or 6 +4? Explain.
Do you think that the order in which we subtract or divide numbers matters? Explain. 1
It does not matter which order we add or multiply numbers in.
4 + 6 = 6 + 4
3 x 5 = 5 x 3
However it does matter which order we subtract or divide numbers in. 6 ­ 3 3 ­ 6
1 2 2 1 Do you know what we call this property?
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Commutative Property of Addition ­ Changing the order of the addends does not change the sum. Ex.: 6 + 3 = 3 + 6
Associative Property of Addition ­ Changing the grouping of addends does not change the sum.
Ex.: (9 + 5) + 4 = 9 + (5 + 4)
(In other words, it does not matter which pair of numbers we add first!)
Identity Property of Addition ­ The sum of 0 and any number is that number.
Ex.: 9 + 0 = 9 3,279 + 0 = 3,279
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Using these Addition Properties for Mental Math
Use mental math to find the total number of students.
Find the sum of 36 + 25 + 34
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Commutative Property of Multiplication ­ Changing the order of factors does not change the product.
Ex.: 4 x 6 = 6 x 4
Associative Property of Multiplication ­ Changing the grouping of the factors does not change the product.
Ex.: (4 x 6) x 2 = 4 x (6 x 2) Identity Property of Multiplication ­ The product of 1 and any number is that number. Ex.: 4 x 1 = 4 56,982 x 1 = 56,982
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Using these Multiplication Properties for Mental Math
Find the product of 4 x 8 x 25
Find 20 x (6 x 5)
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Multiplying by 10, 100, or 1,000
Count the number of total ending zeros in the question.
The product will always have this many zeros.
83 x 100
1,000 x 30
650 x 10
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Now, You're on Your Own...
(17 + 24) + 183 + 0
25 x 13 x 4
837 + 14 + 26
20 x 1 x (19 x 50)
Is subtraction or division commutative? Associative? Explain with examples.
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