Properties of Operations Pre-Assessment
Task:
Read statements 1) and 2) below . For each statement:




Circle (S) if the statement is Sometimes true.
Circle (A) if the statement is Always true.
Circle (N) if the statement is Never true.
Circle (DK) if you Don’t Know.
Sometimes, Always, Never
S
A
N
DK
S
A
N
DK
1. If a is a real number, it has a multiplicative inverse.
2. If a is a real number, it has an additive inverse.
For numbers 3 and 4, circle (T) if the statement is true and (F) if the statement is false. Circle
DK if you don’t know.
True or False?
T
T
F
F
DK
3. For all real numbers, a and b, the commutative property
of multiplication assures that a x b = b x a.
DK
4. The set of whole numbers is closed under subtraction,
i.e., for any two whole numbers, a and b, a – b is a
whole number.
1
Below is a list of properties of operations:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Associative property of addition
Commutative property of addition
Additive identity property of 0
Additive inverse
Associative property of multiplication
Commutative property of multiplication
Multiplicative identity property of 1
Multiplicative inverse
Distributive property of multiplication over addition
Below are the steps in the solution of a linear equation. Some of the reasons for the steps are
completed. Others are left blank. Please place in the blank the number of the property from
above that justifies the step. Numbers may be used more than once and some numbers
may not be used. If you don’t know, put DK in the blank.
3x – 5 + x = 7
Given equation
3x + (-5) + x = 7
Definition of subtraction
3x + x + (-5) = 7
__________
(3 + 1) x + (-5) = 7
__________
4x + (- 5) = 7
Addition fact
(4x + (-5)) + 5 = 7 + 5
Addition property of equality
(4x + (-5)) + 5 = 12
Addition fact
4x + (-5 + 5) = 12
__________
4x + 0 = 12
__________
4x = 12
__________
¼ (4x) = 12 (¼)
Multiplication property of equality
¼ (4x) = (3 . 4) (¼)
Multiplication fact
(¼ . 4)x = 3 (4 . ¼)
__________
1x = 3 . 1
__________
x=3
__________
2