Transcript Math Properties

𝐴∗𝐵 =𝐵∗𝐴
Math Properties
Commutative, Associative,
Distributive, and Identity Properties
What are properties?
• In life, there are rules and laws that tell us
what we can and can not do. . .
• In math, properties are like those laws or
rules they tell us what we can and can not
do with sets of numbers
Commute
• To commute means to travel from one place
to another.
• For example, you commute to school in the
morning.
Commutative Property
• Just like you commute from home to school, a
number may commute from one spot to
another.
• a + b = b + a (The numbers change places.)
• This is called the commutative property of
addition.
• Ex) 2 + 3 = 3 + 2
• Both 2 + 3 and 3 + 2 equal 5.
Commutative Property
• The commutative property may be used with
addition as seen previously and also with
multiplication.
• a·b=b·a
• Ex) 3 · 5 = 5 · 3
• Both 3 · 5 and 5 · 3 equal 15.
• This is called the commutative property of
multiplication.
Associate
• An associate is a friend or someone
you work with.
• For example, the head cheerleader is
an associate of the school mascot.
Now imagine the football team played a late game
and the cheerleader and mascot forgot to study for
the math test.
Suddenly the cheerleader associates
with someone else.
Associative Property
The associative property is when a number
associates with a different number.
A + (B + C) = (A + B) + C
or
2 + (6 + 5) = (2 + 6) + 5
Associative Property
• says that when we ADD or MULTIPLY sets of
numbers, how we (GROUP) THEM DOES NOT
MATTER because our answer will be the same
• Grouping” means putting numbers inside
(parentheses)
• (A + B) + C = A + (B + C) is called the
associative property of addition.
• Ex) (2 + 3) + 4 = 2 + (3 + 4)
Associative Property
• The associative property may be
used with addition as seen
previously and also with
multiplication.
• A · (B · C) = (A · B) · C is called the
associative property of
multiplication.
A few notes about the associative and
commutative properties. . .
• They DO NOT APPLY to subtraction and division
because grouping and ordering numbers using those
operations DOES CHANGE THE ANSWER
– Look at 1, 2, and 3.
• Solve: 1 – 2 – 3 =
• Then solve: 2 – 1 – 3 =
• Are the answers the same?
• Who can name the main difference between the two
properties?
• Answer: The presence of parentheses is always with
the associative property!
So let’s try a few. . .
•
•
•
•
•
Name that property!
1) (34 · 24) · 55 = 34 · (24 · 55)
2) 46 + (92 + 3) = (3 + 46) + 92
3) 76 · 23 · 1 = 1 · 23 · 76
4) What is the difference between
number 2 and 3?
Identity
• Your identity is who you are.
• Changing your clothes or getting a
new haircut does not change your
identity.
• Your identity remains the same.
Property of Addition
• A number also has an identity
• The identity of a number is the value of the
number
• The additive identity is the number that when
added to another number does not change
the identity of the original number
• 3 + __
0 = 3 (What goes in the blank?)
Zero
• The additive identity is zero.
• We can add zero to any number
and the answer is the original
number.
Identity Property of Multiplication
• We also have a multiplicative identity
1 = 3 (What goes in this blank?)
• 3 · __
• We can multiply any number by one and the
answer will be the original number.
Identity Properties
Identity Property of Addition
A+0=A
Identity Property of Multiplication
A·1=A
Distribute
• Distribute means to deliver or pass out
• If we distribute food to three boxes, we put
food in each of the three boxes
Distributive Property
• The A is the food and the boxes are B and C.
• We pass out A to each of B and C.
• In this case that means that we multiply A by
both B and C separately and then add the
resulting products.
• Ex) 4(2 + 3) = 4 · 2 + 4 · 3
= 8 + 12
4·5
= 20
20
Now you try these examples.
1) 5(6 + 3) = 5 · 6 + 5 · 3
2) 7(2 + 4) = 7 · 2 + 7 · 4
3) 2(6 -3) = 2 · 6 – 2 · 3
So let’s try a few. . .
• Fill in the blank.
• 5) 4(2+10) = ______________
• 6) 9(12+15) = _____________
• 7) __________ = 8 · 10 + 8 · 17
• 8) __________ = 12 · 4 + 12 · 7
Now you try. . . (in class work!)
• Identify the property.
–9. (12 · 4) · 9 = (4 · 9) · 12
–10. 88 + 12 + 87 = 12 + 87 + 88
–11. 3(50 + 10) = 3 · 50 + 3 · 10
–12. 45 · 88 · 16 = 88 · 45 · 16
Now you try. . . (in class work!)
• Fill in the blanks then identify the
property.
–13. ____________ = (87 · 23) · 19
–14. 13(3 + 5) = ______________
–15. _________ = 6 · 7 + 6 · 8
–16. 99 + 12 + 34 = _____________
–17. What two operations do the
associative and commutative property
NOT apply to? Explain why.