Download Substitution Property – If a = b then you can replace b with a

Lesson 1.4 Properties (p. 23-32)
In algebra, properties are statements that
are true for any numbers.
Substitution Property – If a = b then you
can replace b with a. (p. 18)
Let a = 4
a + 18
4 + 18
Commutative Property – the order in
which you add or multiply numbers does
not matter. (p. 23)
 True for addition and multiplication
3+8=8+3
2•6=6•2
Associative Property – the way in which
you group numbers does not change the
answer when adding or multiplying.(p. 24)
 True for addition and multiplication
(8 + 1) + 10 = 8 + (1 + 10)
3 • (4 • 2) = (3 • 4) • 2
Additive Identity Property – adding 0 to
any number does not change the value of
the number. (p. 24)
17 + 0 = 17
 The identity element (number) for
addition is _______
Multiplicative Identity – multiplying any
number by 1 does not change the value of
the number. (p. 24)
25 = 25 • 1
1•9=9
 The identity element for
multiplication is _____
Multiplicative Property of Zero – zero
times any number equals 0. (p. 24)
34 • 0 = 0
0(6) = 0
Closure Property – applies when an
operation is performed (+ , - , ×, ÷) on a
set of numbers and the answer also falls
within the same set of numbers.
Addition is closed under the set of whole
numbers.
 If you take any two whole numbers
and add them together, the answer
will also be a whole number.
9 + 7 = 16
Subtraction is not closed under the set of
whole numbers.
4 – 8 = -4
-4 is an integer NOT a whole number
Symmetric Property – If one quantity
equals a second quantity, then the second
quantity also equals the first. (p. 29)
If 13 = 7 + 6, then 7 + 6 = 13
Transitive Property - if one quantity equals
a 2nd quantity and the 2nd quantity equals a
3rd quantity, then the 1st equals the 3rd.
(p. 29)
If 3 + 5 = 8 and 8 = 2(4),
Then __________________
Reflexive Property – any quantity is equal
to itself.
For any number a, a = a