Question Lesson Goals · Associative Property Identity Property Distributive Property The of...
Transcript of Question Lesson Goals · Associative Property Identity Property Distributive Property The of...
© Edgenuity, Inc. 1
Warm-Up Using Properties of Operations
Lesson Question
Lesson Goals
Evaluateexpressions.
property of operationsto rewrite expressions.
Use the Use the
property of operationsto rewrite expressions.
Use the commutativeproperty of operationsto rewrite expressions.
Words to Know
Fill in this table as you work through the lesson. You may also use the glossary to help you.
evaluate to determine the of
associative property
the property stating that the way in which two or
more numbers are in a sum or
product does not change the value
commutative propertythe property stating that changing the
in which two numbers are added or multiplied does not change the value of the sum or product
?
WK2
© Edgenuity, Inc. 2
Warm-Up Using Properties of Operations
Words to KnowWK2
distributive property
the property stating that the of a factor
times a given quantity containing a sum or difference is
equal to the of the products of that factor
times each addend from within the quantity
identity property
the property stating that an operation performed between a number and the identity element
( in addition and 1 in ) will
result in the same number
© Edgenuity, Inc. 3
Instruction Using Properties of Operations
Properties of Operations
Commutative Property
• Addition: a + b = b +
• 3 + 2 = 2 + 3
5 =
• Multiplication: a(b) = b(a)
• 3(2) = 2(3)
6 6
Associative Property
The associative property changes where the parentheses lie.
• : a + (b + c) = (a + b) + c
• 3 + (5 + 1) = (3 + 5) + 1
3 + 6 = + 1
9 = 9
• Multiplication: a(bc) = (ab)c
• (3)[5(1)] = [3(5)](1)
(3)(5) = 15(1)
= 15
2Slide
© Edgenuity, Inc. 4
Instruction Using Properties of Operations
Using the Commutative and Associative Properties
Commutative property of addition:
a + b = b + a
4 + 7 + 6 =
11 + 6 =
4 + 6 + 7 =
+ 7 = 17
Associative property of multiplication:
(bc) = (ab)
(5)[2(7)] =
[5(2)]( )
10(7) = 70
property of
addition:
a + b = b + a
property of
addition:
a + (b + c) = (a + b) + c
Evaluate the expression using both properties:
2 + (4 + 8) = 2 + ( + )
= (2 + 8) + 4
= 10 + 4
=
2Slide
The problem can be made simpler using the commutative property. Switch the 7 and 6.
© Edgenuity, Inc. 5
Instruction Using Properties of Operations
4Slide
The Identity Property
Identity Property
• Addition:
• a + 0 = a
14 + 0 =
• Multiplication:
• a(1) = a
14( ) = 14
• Nonexamples:
• a + 1 = a + 1
14 + 1 = 14 + 1 =
• Property of Zero
• a(0) = 0
14(0) =
The Properties of Operations
The distributive property states that a number times a sum is the as the sum of the number times each addend.
a(b + c) = a( ) + a(c)
2(5 + 7) = 2(5) + 2( )
2( ) = 10 + 14
24 =
Let a = 14.
7
© Edgenuity, Inc. 6
Instruction Using Properties of Operations
The Distributive Property
Use expanded form and the property to simplify the multiplication.
4(53)
4( + )
4(50) + 4(3)
200 + 12 =
Combining Properties of Operations
Evaluate the expression. Use the properties of operations to make the
calculations .
15 + (12 + 35)
15 + (35 + 12)
(15 + 35) + 12
+ 12 =
9Slide
12
commutative property
property
© Edgenuity, Inc. 7
Instruction Using Properties of Operations
Use the properties of operations to evaluate this expression.
18 + 3(64)
18 + 3(60 + 4)
18 + 3(60) + 3(4)
18 + 180 + 12
18 + + 180 = 30 + 180 =
By combining properties of operations, we can take a more complicated problem and simplify it.
property
property
12Slide
© Edgenuity, Inc. 8
Summary
? Lesson Question
Using Properties of Operations
? Lesson Question
How can you use properties of operations to evaluate expressions?
Answer
Review: Key Concepts
Commutative Property
Associative Property
Identity Property
Distributive Property
The
of addition or multiplication can be switched.
The
in addition and multiplication can be switched.
Addition by 0 and multiplication by 1 does not change the value of the number.
Multiplying a sum by a number is the same as the sum of the number times each addend.
3 + 5 = 5 + 3 (3 + 5) + 7 = 3 + (5 + 7) 5 + = 5 3(5 + 7) = 3(5) + 3(7)
4(24) = 4(20) + 4(4)3(5) = 5(3) [3(5)]7 = 3[5(7)] 5(1) =
2
© Edgenuity, Inc. 9
Summary Using Properties of Operations
Properties of operations:
• Commutative property
• Addition and
• property
• Addition and multiplication
• Identity property
• and multiplication
• property
Use this space to write any questions or thoughts about this lesson.
2Slide