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7th Grade Math / Lesson 3: Properties

PROPERTIES
What will we be learning in this unit?


  • This lesson will explain the different properties for adding and multiplying.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


Properties
Commutative Property


The commutative property for addition says that the order in which you add numbers does not matter.

Ex) 6 + 7 = 7 + 6

The commutative property for multiplication says that the order in which you multiply numbers does not matter.

Ex) 4 * 2 = 2 * 4


Properties
Associative Property


The associative property for addition says that the way you group numbers to be added does not matter.

Ex) (65 + 21) + 33 = 65 + (21+ 33)

The associative property for multiplication says that the way you group numbers to be multiplied does not matter.

Ex) (5 * 2) * 6 = 5 * (2 * 6)


Properties
Distributive Property


The distributive property is when you take a factor and spread it out over a sum (or difference).

Ex) 2 ( x + 4 ) = 2 * x + 2 * 4 = 2x + 8

Ex) 5 ( 4 - x ) = 5 * 4 - 5 * x = 20 - 5x


Properties
Identity Property


The identity property for additionsays that zero added to another number is always the other number.

Ex) 12 + 0 = 12

The identity property for multiplication says that one multiplied by any number is always the other number.

Ex) 35 * 1 = 35


Properties
Zero Property of Multiplication


The zero property of multiplication says that when you multiply by zero, the result is zero.

Ex) -64 * 0 = 0

Ex) 0 * 47 = 0


Properties
Inverse Property


The inverse property of addition says that when you add opposites the result is always zero.

Ex) -64 + 64 = 0

The inverse property of multiplication says that when you multiply reciprocals* the result is one.

Ex)     4/5 *5/4      = 1

* reciprocals are the numbers you get when you flip a number. In other words you take the numerator and make it the denominator and take the denominator and make it the numerator. 2 and  ½ are reciprocals.


Properties


For a self-check on identifying the properties, click  HERE. Close the page by clicking on the x in the top right corner when you are ready to return to the lesson slide.