Basic Algebraic Properties

By Daphne Sakavellas

Edited by Danika Suh


The Associative Property states that you can add or multiply numbers no matter how they are grouped. If you are adding or multiplying, it does not matter where the parentheses are.


The Commutative Property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. It applies to addition and multiplication, but not to subtraction or division.


For Addition, the rule is

a + b = b + a.


Ex.) 7 + 9 = 9 + 7

{7+9 = 16; 9+7 = 16}


For Multiplication, the rule is

ab = ba


Ex.) 7 x 9 = 9 x 7

{7 x 9 = 63; 9 x 7 = 63}


The Distributive Property allows you to multiply a sum by multiplying each addend separately and then adding the products.


Ex.) 7(3+7) = (7 x 3)+(7 x 7)

7 x 3 = 21

7 x 7 = 49

21 + 49 = 70



Sources Cited:

https://www.mathwarehouse.com/dictionary/D-words/distributive-property-definition-and-examples.php

https://www.purplemath.com/modules/numbprop.htm

https://www.mathwarehouse.com/dictionary/A-words/definition-of-associative-property.php

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