FL.MA.6.A.3.5
Apply the Commutative, Associative and Distributive Properties to show that two expressions are equivalent.
-ALL WORK MUST
FCAT Packet # 6
BE SHOWN ON A
Property
Definition
Example
SEPARATE SHEET OF
Distributive
To multiply a sum by a number, multiply
2 (7 + 4) = 2 • 7 + 2 • 4
PAPER!
Property
each addend by the number outside the
Associative
Properties
Commutative
Properties
Identity
Properties
parenthesis.
The way in which three numbers are
grouped when they are added or multiplied
does not change their sum or product.
The order in which two numbers are added
or multiplied does not change their sum or
product.
The sum of the addend and 0 is the
addend.
The product of a factor and 1 is the factor.
3+(9+4)=(3+9)+4 or a+(b+c) = (a+b)+c
8(5x7) = (8x5)7 or a(b•c) = (a•b)c
7+9 = 9+7 or a+b = b+a
4x6 = 6x4 or a • b = b • a.
13+0=13 a +0= a
-NUMBER ALL
PROBLEMS AND
CIRCLE ALL
ANSWERS!
-PUT ALL ANSWERS
IN THE ANSWER
COLUMN.
7 •1 = 7 a •1 = a
Examples
Use properties to determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
72 – (63 – 8) = (72 – 63) – 8
72 – 55 = 9 - 8
17 ≠ 1
Changing the grouping (associative property) does not
apply to subtraction because 17 is not equal to 1.
7 • 25• 8 = 25 • 7 • 8
175 • 8 = 175 • 8
1400 = 1400
Changing the order (commutative property) does not
change the product.
Use properties to determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
1.
15+(5+8)=(15+5)+8
2.
(20-12)-3 = 20-(12-3)
3.
34+0=34
4.
20÷5 and 5÷20
----------------------------------------------------------------------------------------------------------------- ------------------------------------------------Applying Properties to Word Problems
Example
The Florida Gators have 5 guards, 6 forwards, and 1 center on their roster. Write two equivalent expressions using the Associative
Property that can be used to find the total number of players on their roster.
(5 + 6) + 1 = 5 + (6 + 1)
11 + 1= 5 + 7
12 = 12 √
5. Samantha earned $7.00 babysitting and $12.00 cleaning. Write two equivalent expressions using the Commutative Property that can
be used to find the total amount she earned.
6. At a gymnastic meet a gymnast scored 8.95 on the vault and 9.2 on the uneven bars. Write two equivalent expressions that could be
used to find her total score.
7. Each day, about 75,000 people visit Paris, France. Use the commutative property to write two equivalent expressions that could be
used to find the number of people that visit over a 5-day period.
8. Ella sold 37 necklaces for $20.00 each at the craft fair. She is going to donate half of the money she earned to charity. Use the
commutative property to mentally find out how much money she will donate. Explain the steps you used.
----------------------------------------------------------------------------------------------------------- ------------------------------------------------------Distributive Property
2 x (3 + 4) = 2 x (3 + 4) = (2 x 3) + (2 x 4) = 6 + 8 = 14
Try these on your own: 9)
7 x (8 + 1) =
10)
6(5 – 2) = 6(2 – 5) = (6 x 5) – (6 x 2) = 30 – 12 = 18
4(9 + 3) =
11) 5 x (6 – 4) =
12)
2(2 – 1) =
13. Show the how the distributive property combines addition and multiplication to express the word problem- Three friends went to
a baseball game. Each ticket cost $20.00 and all three friends bought a baseball hat for $15.00 each.
14.
18.
19.
20.
15.
21.
16.
17.