Download - Properties of Addition
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Properties of Addition
Lesson 1-4
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Three Properties of Addition
1. Commutative2. Associative3. Identity
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The Commutative Property
• Background– The word commutative comes from the
verb “to commute.”– Definition on dictionary.com
• Commuting means changing, replacing, or exchanging
– People who travel back and forth to work are called commuters.• Traffic Reports given during rush hours are
also called commuter reports.
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Here are two families of commuters.
Commuter A
Commuter B
Commuter ACommuter
B
Commuter A & Commuter B changed lanes.
Remember… commute means to change.
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Here is another example…
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Think of this hypothetical situation:
Every day you ride your bike to school. The distance from home to school is 2 miles.The distance from school to home is also 2 miles.How do we know this?
Did you notice that hypothetical and hypothesis look almost the same?
Hmmmm... Think about what hypothesis means…
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Home School
The distance from Home to School is the same as the distance from school to home.
Home + School = School + Home
H + S = S + HA + B = B + A
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The Commutative Property
A + B = B + A
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Three Properties of Addition
1. Commutative2. Associative3. Identity
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The Associative Property
• Background– The word associative comes from the
verb “to associate.”– Definition on dictionary.com
• Associate means connected, joined, or related
– People who work together are called associates.• They are joined together by business, and
they do talk to one another.
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Let’s look at another hypothetical situation
Three people work together.
Associate B needs to call Associates A and C to share some news.
Does it matter who he calls first?
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A C
B
Here are three associates.
B calls A first He calls C last
If he called C first, then called A, would
it have made a difference?
NO!
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(The Role of Parentheses)
• In math, we use parentheses to show groups.
• In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS)
So….
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The Associative Property
(A + B) + C = A + (B + C)
A C
B
A C
B
THEN THEN
The parentheses identify which two associates talked first.
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Three Properties of Addition
1. Commutative2. Associative3. Identity
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The Identity Property of AdditionI am me!
You cannot changeMy identity!
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Zero is the only number you can add to something
and see no change.
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Identity Property of Addition
A + 0 = A
+ 0 =
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Let’s practice !
Look at the problem.
Identify which property it represents.
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(9 + 8) + 7 = 9 + (8 + 7)
The Associative Property of Addition
It is the only addition property that has parentheses.
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12 + 0 = 12
The Identity Property of Addition
It is the only addition property that has two addends and one of them is a zero.
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9 + 7 = 7 + 9
The Commutative Property of Addition
It is the only addition property that has numbers that change places.
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4 + 6 = 6 + 4The Commutative Property of Addition
Numbers change places.
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3 + 0 = 3 The Identity Property of Addition
See the zero?
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(4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition
It has parentheses!
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a + 0 = a The Identity Property of Addition
Zero!
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a + b = b + aThe Commutative Property of Addition
Moving numbers!
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A
(a + b) + c = a + (b + c) The Associative Property of Addition
Parentheses!
C
B