Commutative/Associative Properties

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Study Guide Commutative/Associative Properties Mathematics, Grade 6

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What Are Commutative and Associative Properties? Commutative Property: The commutative property allows us to change the order of the numbers without changing the outcome of the problem. The order of the numbers (addends) does not affect the sum. Therefore, 6 + 10 = 10 + 6.The words commuter and commutative come from the same root word, “commute,” which means “to exchange for another.” Associative Property: The associative property allows us to change the grouping of the numbers. The associative property refers to adding or multiplying 3 or more addends or factors. Pairs of numbers are added and the sum is added to the third number. For example, 12 + 3 + 10 can be solved by adding 12 + 3 which equals 15 and then adding 15 + 10 which equals 25. The same sum results if the numbers are added in a different set of pairs, 3 + 10 = 13 and 13 + 12 = 25. Other examples of the associative property include: 14 + (5 + 24) = (14 + 5) + 24 = 43 (20 + 30) + 9 = 20 + (30 + 9) = 59 (3 X 6) X 20 = 3 X (6 X 20) = 360 15 X (8 X 1) = (15 X 8) X 1 = 120 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
The associative property allows us to choose the first two numbers to add or multiply. Sometimes, the first two numbers added equal a sum of 10 or 20 or 100. This makes it easier to add the third number. Sometimes, the sum or product is known quickly and so speeds the process of adding or multiplying more than two numbers. Neither the commutative property nor the associative property can be applied to subtraction or division. These two properties apply only to multiplication and addition. How to figure out Commutative Property and Associative Property problems: When adding or multiplying, the order of the numbers is irrelevant. The same sum or product will be the result, regardless of the order of the numbers: 145 + 240 = 240 + 145 = 385 36 X 20 = 20 X 36 = 720 Try This! Write another way to calculate and solve: 41 + 65? ________________ Write another way to calculate and solve: 68 X 35 ________________ Apply the associate law and solve: 5 + 12 + 28 ________________ Apply the distributive law and solve: 12 + 50 + 23 ________________ Apply the distributive law and solve: 40 + 25 + 9 _________________ © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.