CCA Lesoon 3.2.4 Methods and Meanings Properties of Real Numbers

CCA Lesoon 3.2.4 Methods and Meanings Properties of Real Numbers

Learning Target:​

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Students will understand the different properties of real numbers to be able to simplify numerical and algebraic expressions and solve equations.

​Commutative Property

he Commutative Property states that when adding or multiplying two or more numbers or terms, order is not important.  That is:

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​However, subtraction and division are not commutative, as shown below.

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​Associative Property

​The Associative Property states that when adding or multiplying three or more numbers or terms together, grouping is not important.  That is:

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However, subtraction and division are not associative, as shown below.

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​Identity Property

​The Identity Property of Addition states that adding zero to any expression gives the same expression.  That is:

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The Identity Property of Multiplication states that multiplying any expression by one gives the same expression.  That is:

​Inverse Property

​Distributive Property

Multiple Choice

Identify the property
a + b = b + a

• Identity of addtion
• commutative of addition
• associative of addition
• symmetric

Multiple Choice

Identify the property
(a ⋅ b) ⋅ c = (c ⋅ b) ⋅ a

• commutative of multiplication
• identity of multiplication
• inverse of multiplication
• associative of multiplication

Multiple Choice

Identify the property
a + 0 = a

• identity of addition
• identity of multiplication
• inverse of addtion
• multiplication of zero

Multiple Choice

Pick the answer that is an example of the commutative property of multiplication

• b + c + a = a + b + c
• a(b + c) = ab + ac
• a ⋅ b = b⋅ a
• a ⋅ 1 = a

Multiple Choice

Pick the answer that is an example of the identity property of multiplication?

• $$a\ \cdot\ 1\ =\ a$$

• $$a\ \cdot\ 1\ =\ 1$$

• $$a\ \cdot\ 0\ =\ 0$$

• $$a\ \cdot\ \frac{1}{a\ }\ =\ 1$$

Multiple Choice

Identify the property
a(b + c) = ab + ac

• Associative of addtion
• Distributive
• Commutative of addition
• Inverse

Multiple Choice

Which is an example of the commutative property of multiplication?

• 4 x(1 _^x 2) = (4 x 1) x 2
• 2 x 2 = 4 x 1
• 2(3) = 2(4)
• 3 x 4 = 4 x 3

Multiple Choice

The commutative property of multiplication states that the order of the numbers in an equation:

• Should go from least to greatest
• Doesn't change the product
• Should go from greatest to least
• Is always important

Multiple Choice

Which of these illustrates the associative property of multiplication?

• 4 x (5 x 6) = (4 x 5) x 6
• 6 (9 + 1) = (6 x 9) + (6 x 1)
• 4 x (56) = (45) x 6
• 5 + 0 = 0 + 5

Multiple Choice

Rewrite (9 x 6) x 5 using the associative property.

• 270
• 9 x 30
• 9 x (6 x 5)
• 5 x 9 + 5 x 6

Multiple Choice

9+0=9

• Commutative Property of Addition

• Associative Property of Addition

• Identity Property of Addition

• Additive Inverse Property

Multiple Choice

Which property is represented?
2(4 + 9) = 8 + 18

• Commutative Property
• Associative Property
• Distributive Property

Multiple Choice

Every time Mike adds zero to another number it stays the same.  What property is Mike using?

• Identity Property of Addition
• Identity Property of Multiplication
• Commutative Property of Addition
• Commutative Property of Multiplication

Multiple Choice

Identity Property of Multiplication

• 1 x 3 = 3
• 7 x 0 = 0
• 12 + 0 = 12
• 2 x 3 = 3 x 2

Multiple Choice

9+(2+4) = (9+2)+4

• Commutative Property of Addition

• Associative Property of Addition

• Additive Identity Property

• Distributive Property

Multiple Choice

The Distributive Property would say
3(a + 2b) = ______

• 3(2b + a)
• (a + 2b)3
• 3a + 2b
• 3a + 6b

Multiple Choice

What is the MULTIPLICATIVE INVERSE of
8

• -8
• ^-1/₈
• ¹/₈
• 1

Multiple Choice

What property is this?

⁴/₅ x ⁵/₄ = 1

• Inverse Property of Multiplication

• Multiplicative Identity

• Commutative

• Associative

Multiple Choice

What is a number that would be involved in EVERY equation involving the identity property of multiplication?

• -1

• 0

• ¹/₂

• 1

Multiple Choice

What is the reciprocal of 2/3?

• -2/3
• 3/2
• -3/2
• 2/3