Transcript Math Properties - Roselle Borough Public Schools

𝐴∗𝐵 =𝐵∗𝐴
Math Properties
Commutative, Associative,
Distributive, Identity, and Zero
Properties
What are properties?
Math Properties are rules in math.
Properties are always true for every
number.
**Once you go beyond the set of Real numbers the properties may no longer hold.
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.
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
(A + B) + C
Associative Property
• (A + B) + C = A + (B + C) is called the
associative property of addition.
• Ex) (2 + 3) + 4 = 2 + (3 + 4)
• The order in which you add does not change
your answer.
• A * (B * C) = (A * B) * C is called the
associative property of multiplication.
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.
Identity 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
Zero Property
• The zero property sounds just like what it is, a
property about zero.
• A*0=0
• The zero property tells us that any number
multiplied by zero equals zero.
Summary
Property Name
Rule
Commutative Property of Addition
A+B=B+A
Commutative Property of Multiplication
A*B=B*A
Associative Property of Addition
A + (B + C) = (A + B) + C
Associative Property of Multiplication
A * (B * C) = (A * B) * C
Identity Property of Addition
A+0=A
Identity Property of Multiplication
A*1=A
Zero Property
A*0=0
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
•
•
•
•
A(B + C) = A*B + A*C
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(X + 3) =4X + 12
4
X
4X
3
12
Now you try these examples.
1) 5(X + 3) = 5X + 15
2) 7(X + 4) = 7X + 28
3) 2(Z -3) = 2Z - 6
Summary
Property Name
Rule
Commutative Property of Addition
A+B=B+A
Commutative Property of Multiplication
A*B=B*A
Associative Property of Addition
A + (B + C) = (A + B) + C
Associative Property of Multiplication
A * (B * C) = (A * B) * C
Identity Property of Addition
A+0=A
Identity Property of Multiplication
A*1=A
Zero Property
A*0=0
Distributive Property
A(B + C) = A*B + A*C
Solve these in your notebook
1 ) Which equation shows the Commutative Property of Multiplication ?
A. 6 x 8 - 4 x 8 = (6 - 4) x 2
B. 5 x 1 = 5
C. 2 x 3 = 2 + 2 + 2
D. 7 x 3 = 3 x 7
2 ) Which property is used in the following ? 8 x (7 + 5) = 8 x 7 + 8 x 5
A. Commutative Property
B. None of the above
C. Distributive Property
D. Associative Property
3 ) Which is an example of Associative Property of Addition ?
A. 6 + (-6) = 0
C. ( 4 + 9) + 5 = 4 + (9 + 5)
B. 2 + 0 = 2
D. 3 + 4 = 4 + 3
4) Which of the following does not show the Commutative Property ?
A. x + y = y + x
B. 4 + y = y + 4
C. yx = xy
D. xy - 3 = xy
5 ) Which equation shows the Identity Property of Multiplication ?
A. a(b + c) = ab + ac
B. a x 1
C. (a + b) + 5 = a + (5 + b)
D. a + a + a = 3 x a
6 ) Which Property of Multiplication is shown ? (5 + 9) x 7 = 5 x 7 + 9 x 7
A. Commutative Property
B. Associative Property
C. Distributive Property
D. Identity Property
7 ) Which of the following does not show the Commutative Property of Addition ?
A. a + b = b + a
B. 3x + 4y = 4y + 3x
C. b = ba
D. 4 + x = x + 4
8 ) Which Property of Addition does 7 + 0 = 7 illustrate ?
A. Zero Property
C. Distributive Property
B. Commutative Property
D. Identity Property