Overview: Properties of Addition and Multiplication
The commutative and associative properties of addition and multiplication are useful within operations. Both properties help students to arrange and group numbers more effectively. However, these properties do not hold for either subtraction or division.
What Is the Commutative Property?
The commutative property of addition and multiplication states that any numbers a and b can be added (or multiplied) in any order to equal the same amount. In other words (or symbols) , a + b = b + a. For example, 4 + 5 = 5 +4. It forms a shortcut for basic addition facts.
What Is the Associative Property?
While the commutative property states that order that numbers are added doesn’t matter, the associative property states that the way numbers are grouped doesn’t matter, as long as everything is being added. Therefore, (a + b) + c = a + (b +c). If a equals 4, b equals 5, and c equals 3 , (4 + 5) +3 = 4 +(5 +3).
How Are the Properties Used Together?
The properties can be used together to solve problems. For example, if the order doesn’t matter when adding numbers together, and the way numbers are grouped doesn’t matter, one can use shortcuts when adding. In fact, both properties are used when adding two-digit numbers without much thought. For example 46 +33 = 79. That is the same as (40 + 6) + (30 + 3) = (40 +30) + (6 + 3) or 70 +9 = 79. The numbers have been expanded into what they mean, grouped together, and rearranged.
Why Are They True for Multiplication?
The commutative and associative properties are true for multiplication, because one definition for multiplication is repeated addition. If 3 X 3 means the same thing as 3 + 3 + 3, then multiplication is a shortcut that involves grouping numbers differently. For example, 24 X 36 = 864 , which equals (24 X 30) + (24 X 6) = 720 + 144 = 864.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Houston, TX visit: Tutoring in Houston, TX