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Lesson 1-4: Identity and Equality Properties
Property
Name
Additive
Identity
or
Identity (+)
Multiplicative
Identity
or
Identity (  )
Multiplicative
Property of
Zero
(there is NO
abbreviation
for this)
Multiplicative
Inverse
Property
Reflexive
Property
Symmetric
Property
Transitive
Property
Substitution
Property
Symbols
Examples
Lesson 1-4 Properties
40  4
a0  0a  a
0  10  10
4x  0  4x
a 1  1 a  a
1(9)  9
5 1  5
yz  1  yz
a 0  0 a  0
0(9)  0
x0  0
2b  0  0
a b
 1
b a
b a
 1
a b
For any number a, a = a.
2 3
 1
3 2
1
3  1
3
1
 25  1
25
bb
99
cd cd
For any numbers a and b, if a = b, then (1) If 4  2  6 , then
b = a.
6  42.
(2) If x  2  8 , then
8  x  2.
(3) If 3b  21 , then 21  3b .
For any numbers a, b and c, if a = b
(1) If a  6 , and 6  3  2 ,
and b = c, then a = c.
then a  3 2 .
(2) If 5  7  8  4 , and
8  4  12 , then 5  7  12 .
(3) If a  9 , and 9  b , then
a  b.
If a = b, then a may be replaced by b (1) If n = 15, then 3n  3(15) .
in any expression.
(2) Replacing 3 2 with 6 in
an expression.
(3) Replacing 12 – 4 with 8
in an expression.
Meaning in
Your Words
Distributive
Property
Commutative
Property of
Addition
or
Commutative
(+)
Commutative
Property of
Multiplication
or
Commutative
( )
Associative
Property of
Addition
or
Associative
(+)
Associative
Property of
Multiplication
or
Associative
( )
Lesson 1-5 Property
For any numbers a, b, and c,
4(9  7)  4  9  4  7
a(b  c)  ab  ac and (b  c)a  ba  ca 5( x  8)  5  x  5  8
a(b  c)  ab  ac and (b  c)a  ba  ca
 3(2 x  y )  3  2 x  (3)  y
  6 x  (3 y )
  5x  3 y
Lesson 1-6 Properties
46  64
ab  ba
5  6  10  5  10  6
x  ( y  2)  ( y  2)  x
ab  b a
4(9)  9(4)
5  10  10  5
y  ( z  2)  ( z  2)  y
(a  b)  c  a  (b  c)
*You cannot mix
addition and
multiplication for this
property!
(a  b)  c  a  (b  c)
*You cannot mix
addition and
multiplication for this
property!
(3  5)  9  3  (5  9)
5  (6  2)  (5  6)  2
(3  6)  11  3  (6  11)
3  (6  7)  (3  6)  7
Exercises:
Find the value of n. Then, name the property used in each equation.
1. 6n  6
2. n  1  8
3. 6  n  6  9
4. 9  n  9
5.
3
n 1
4
6. n 12  0
Name the property used in each equation.
7. If 4  5  9 , then 9  4  5.
8. 0  21  21
9. 0(15)  0
10. 1  94  94
11. If 3  3  6 and 6  3  2 , then 3  3  3  2 .
12. 4  3  4  3
13. (14  6)  3  8  3
14. 5 
1
1
5
Evaluate each expression. Name the property used in each step.
1  1 2 
15. 2     
 4  2  
17. 2(6  3  1) 
1
2
16. 15  1  9  2(15  3  5)
18. 2(3  5  1  14)  4 
1
4
19. 3(5  5  12 )  21  7
20. 10  5  2 2  2  13
21. (From Practice 1-4) Mr. Katz harvested tomatoes from each of four plants. Two other plants
produced four tomatoes each, but Mr. Katz only harvested one fourth of the tomatoes from each of
these.
a. Write an expression for the total number of tomatoes harvested.
b. Evaluate the expression. Name the property used in each step.