Download Let a, b and c be real numbers. Property Addition Multiplication

1.3 Properties of Real Numbers
Let a, b and c be real numbers.
Property
Commutative
Addition
a+b=b+a
Multiplication
a∙b=b∙a
Associative
(a + b) + c = a + (b + c)
(ab) ∙ c = a ∙ (bc)
Identity
a+0=a; 0+a=a
a ∙1 = a , 1 ∙ a = a
Inverse
a + (-a) = 0
a
Distributive Property
1
 1 ; (a  0)
a
a(b + c) = ab + ac
Give the additive and multiplicative inverse of each quantity:
Additive Inverse
Multiplicative Inverse
8
3
−
7
6x, x ≠ 0
y – 3, y≠ 3
Rewrite the expression using the Associative Property
16 + (5 + y)
10(3x)
Rewrite the expression using the Distributive Property -3(10 – x)
Use the Distributive Property to Simplify the Expression
7p – 2p
4𝑚
7
+
𝑚
7
1.3 Properties of Real Numbers
Using Properties of Real Numbers to Solve Equations
Properties of Equality Let a,b, and c be real numbers.
Addition Property of Equality: If a = b, then a + c = b + c
Multiplication Property of Equality: If a = b, then ac = bc
Identify the Property of Real Numbers that Justifies each Step
x+5=3
(x + 5) + (-5) = 3 + (-5)
x + [5 + (-5)] = -2
x + 0 = -2
x = -2
3𝑥 = 15
1
1
( ) 3𝑥 = ( ) 15
3
3
1
(3 ∙ 3) 𝑥 = 5
(1)(𝑥) = 5
x=5