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```ACTIVITY I
Identify the property described and give an example for each property.
If I am multiplying I can group numbers in a product in any way I want.
Property:
Example:
If I am adding I can do it in any order I want.
Property:
Example:
If I am multiplying the sum of two numbers by a given number I can either add first, and
then multiply or multiply each of them by the given number, and then add.
Property:
Example:
If I am adding I can group numbers in a sum in any way I want
Property:
Example:
If I multiply three numbers I can either multiply the first times the second, and then the
third or multiply the second times the third and then by the first.
Property:
Example:
If I multiply a given number by 1 the product is equal to the given number
Property:
Example:
If I add zero to any given number I always get the given number back
Property:
Example:
If I multiply a given number by its reciprocal I always get 1
Property:
Example:
If I multiply zero by a given number I always get zero
Property:
Example:
Algebra I
Page 3 of 12
Session 3
ACTIVITY II
With your team, respond to each of the following in complete sentences. Give specific
numeric examples to illustrate each.
1. Does the commutative property of addition hold if you take a difference of two
numbers?
2. Does the commutative property of multiplication hold for the division of two
numbers?
3. Does the associative property of addition work if one or more of the operations is a
difference?
4. Does the associative property of multiplication work if one or more of the operations
is a division?
5. Can you use the distributive property to properly distribute (2+3)×(4+5)?
Algebra I
Page 4 of 12
Session 3
ACTIVITY III
With your team, name the property or properties illustrated by each statement.
1. 3x + 2 = 3x + 2
2. If 5 + b = 13, then b = 8
3. If 2x = 3y and 3y = -4, then 2x = -4
4. If f – g = n. then f = n + g
5. If 14 =
+ 10, then
+ 10 = 14
6. If j + 3 = 10, then 4(j + 3) = 4(10)
7. Given: m = n
m= 75
Conclusion: n = 75
8. Given: 7x = 63
Conclusion: x = 9
9. Given: 2x + y = 70
y = 3x
Conclusion: 2x + 3x = 70
Algebra I
Page 5 of 12
Session 3
Activity IV
Work with your team to complete each of the following.
Identify which property of real numbers is being used.
1. x (yz) = x (zy)
2. 2 (x + y) = 2x + 2y
3. (x + y) + z = (y + x) + z
4. 2 [x (a + d)] = [2x] (a + d)
5. 5a + (-5a ) = 0
6. 2
+5
= (2 + 5)
7. (2 )( ) = 2
8. 3
=1
Justify each step using the properties of real numbers and the properties of equality.
An example is given.
Example:
Given: 15y + 7 = 12 - 20y
Conclusion: y =
Statement
Reason
15y + 7 = 12 - 20y
Given
35y + 7 = 12
35y = 5
y =
Subtraction Property of Equality
Division Property of Equality
Algebra I
Page 6 of 12
Session 3
1. Given: 27 = -9(y + 5)
Conclusion: y = -8
Statement
Reason
27 = -9(y + 5)
27 = -9y - 45
72 = -9y
-8 = y
y =
2. Given:
Conclusion: b =
Statement
Reason
3. Given:
Conclusion: x = -2
Statement
Reason
-
b=
2– 12b = 1
-12b = -1
b=
-6 -6(x + 3) = 6
-6 - 6x -18 = 6x
-6x – 24 = 6x
-24 = 12x
-2 = x
x = -2
Algebra I
Page 7 of 12
Session 3
Activity V
End-of-Instruction Assessment
1. A student tried to solve the following equation but made a mistake.
Step 1: 9 − 5(2x + 1) = −28
Step 2: 4(2x + 1) = −28
Step 3: 8x + 4 = −28
Step 4: 8x = −32
Step 5: x = −4
a) In which step did the mistake first appear?
b) Correct the mistake and find the value of x.
2. Complete the missing steps. State the name of the properties used.
Reasons
Step 1. 5(6x + 4) + 1 = −39
Step 2. ________________
___________________________
Step 3. 30x + 21 = −39
___________________________
Step 4. ________________
___________________________
Step 5. x = −2
___________________________
3. Perform the indicated operation: -6(a -7). State the name of the property used.
4. Write the additive inverse of the expression a – b.
5. Use the Associative Law of Multiplication to rewrite the expression
6x(4
6. Use the Commutative Law of Addition to rewrite the expression
7x + 5
Algebra I
Page 8 of 12
Session 3
7. If -10x + 12 = 9, then -5x + 6 = ______________
8. Is the equation 3(2 x− 4) =−18 equivalent to 6x−12 = −18?
A. Yes, the equations are equivalent by the Associative Property of Multiplication.
B. Yes, the equations are equivalent by the Commutative Property of
Multiplication.
C. Yes, the equations are equivalent by the Distributive Property of Multiplication
D. No, the equations are not equivalent.
9. What is the multiplicative inverse of
?
A. −2
B.
C.
D.
10.
2
If 2n = 6, what property of equality justifies writing
p + 2n = 4p + 15 as p + 6 = 4p + 15
A.
B.
C.
D.
11.
Which property justifies rewriting
3x – 5x as (3 – 5)x
A.
B.
C.
D.
12.
Transitive property
Symmetric property
Substitution property
Associative property of multiplication
Distributive property
Commutative property of multiplication
The statement “If
A.
B.
C.
D.
x = 6, then x = 18” is justified by the __________
Associative property of multiplication
Commutative property of multiplication
Multiplication property of equality