1-3 Properties of Real Numbers

1-3 Properties of Real Numbers

by Larry Lawson

​Complete each warm up question in your notebook. You may quietly discuss with your group.

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When I say "Stand Up, Hand Up, Pair Up" find a partner to share your answers.

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​Then we will discuss as a class.

​Notes - Properties of Equality

​Reflexive: Any number equals itself; a = a

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​Symmetric: For any numbers a and b, if a = b then b = a

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​Transitive: If a = b and b = c, then a = c

​Notes - Example 1

​Identify the property used to justify each statement.

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​If 13 + 25 = 38, then 38 = 13 + 25

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​y + 4 = y + 4

​Notes - Example 1

​Identify the property used to justify each statement.

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​If 13 + 25 = 38, then 38 = 13 + 25 <--- Symmetric Property

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​y + 4 = y + 4 <----- Reflexive Property

Multiple Choice

Choose the correct property that matches this statement:

22 + 7 = 22 + 7

• reflexive

• transitive

• symmetric

Multiple Choice

Choose the correct property that matches this statement:

If 36 = 17 + 9, then 17 + 9 = 36

• reflexive

• transitive

• symmetric

Notes - ​Example 2

​Let's say we have a recipe:

• ​The amount of sugar is equal to the the amount of flour plus 2 tbsp

• ​s = f + 2

• ​The amount of milk is equal to the amount of flour plus 2 tbsp

• ​m = f + 2

• ​What could we say about the amount of sugar and the amount of milk?

Notes - ​Example 2

​Let's say we have a recipe:

• ​The amount of sugar is equal to the the amount of flour plus 2 tbsp

• ​s = f + 2

• ​The amount of milk is equal to the amount of flour plus 2 tbsp

• ​m = f + 2

• ​What could we say about the amount of sugar and the amount of milk?

• ​the amount of sugar is equal to the amount of milk

• ​s = m

• This is called the Transitive Property!

Fill in the Blanks

Fill in the Blank: If 43 + 9 = 10 + 42 and 10 + 42 = 52, then 43 + 9 =

​Notes - Example 3

​Use the given property to complete each statement:

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​y - 21 = ________ ; reflexive property

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​​If 24 + 11 = 9 + 26 and 9 + 26 = z, then 24 + 11 = _____; transitive property

​Notes - Example 3

​Use the given property to complete each statement:

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​y - 21 = y - 21 ; reflexive property

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​If 24 + 11 = 9 + 26 and 9 + 26 = z, then 24 + 11 = z; transitive property

Fill in the Blanks

Use the reflexive property to fill in the blank: 

2m - 1 =

​Notes - Addition Properties

​Additive Identity Property: a + 0 = a

(adding 0 to a number gives you the same number)

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​Additive Inverse Property: a + (-a) = 0

(adding a number with its opposite gives you 0)

Multiple Choice

Which property is this?

34 + 0 = 34

• Additive Zero

• Additive Inverse

Multiple Choice

Which property is this?

14 - 14 = 0

• Additive Zero

• Additive Inverse

​Notes - Multiplication Properties

Multiple Choice

Which property is this?

45 x 1 = 45

• Multiplicative Identity

• Multiplicative Inverse

• Multiplicative Zero

Multiple Choice

Which property is this?

6 x 0 = 0

• Multiplicative Identity

• Multiplicative Inverse

• Multiplicative Zero

Multiple Choice

Which property is this?

$$\frac{2}{3}\cdot\frac{3}{2}=1$$  

• Multiplicative Identity

• Multiplicative Inverse

• Multiplicative Zero

​Notes - Example 4

​Evaluate 4 - 2²  + 8(2)                   

​Notes - Example 4

​Evaluate 4 - 2²  + 8(2)                   Simplify 2²

​                  4 - 4 + 8(2)                   Multiply 8 by 2

​                  4 - 4 + 16                      Additive Inverse (4 - 4 = 0)

​                       0 + 16                      Additive Identity (0 + 16 = 16)

​                             16 <-------------Answer

​Notes - Example 5

​Notes - Example 5

​Notes - Example 6

​Notes - Example 6

​Notes - Associative Properties

​Addition: (a + b) + c = a + (b + c)

​(the way you group your numbers when adding does not change the answer)

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​Multiplication: (a x b) x c = a x (b x c)

​(the way you group your numbers when multiplying does not change the answer)

Multiple Choice

Which property is this?

(1 + 2) + 3 = 1 + (2 + 3)

• Associative

• Commutative

​Notes - Commutative Properties

​Addition: a + b = b + a

​(the order in which you add does not change the answer)

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Multiplication: a x b = b x a

​(the order in which you multiply does not change the answer)

Multiple Choice

Which property is this?

4 + 5 = 5 + 4

• Associative

• Commutative

​Notes - Example 7

​34.50 + 32.50 + 23.25 + 31.75

​Notes - Example 8

​Homework:

​Reveal Online Textbook 1-3

• Complete the online questions (check your answers too)​

• Write your work on a sheet of paper and turn it in when we meet again.