Transcript 1-3 Properties of Numbers Goals: • Recognize the properties of equality and identity. • Recognize the Commutative and Associative Properties.

1-3 Properties of Numbers
Goals:
• Recognize the properties of equality and identity.
• Recognize the Commutative and Associative
Properties.
Vocabulary
• Reflexive Property of Equality – any real number
is equal to itself.
• Symmetric Property of Equality – if a = b, then
b=a
• Transitive Property – if a = b and b = c, then a = c
Vocabulary
• Additive Identity Property – the sum of a
number and 0 is always the number.
• Additive Inverse Property – the sum of a
number and its opposite is always 0.
Vocabulary
• Multiplicative Identity – multiplying by 1 does
not change a number
• Property of Zero – anything multiplied by 0 is 0
• Multiplicative Inverse Property – any number
times its reciprocal is 1
• Property of Opposites – anything multiplied by
-1 is the opposite.
Vocabulary
• Commutative Property – the order that you add
or multiply numbers does not change the
answer.
• Associative Property – the way you group three
numbers when adding or multiplying does not
change the answer.
Evaluate Using Properties
Name the property used in each step.
Substitution: 12 – 8 = 4
Substitution: 15 ÷ 5 = 3
Substitution: 3 – 2 = 1
Evaluate Using Properties
Multiplicative Identity: 3(1) = 3
Multiplicative Inverse:
=4
Answer: 4
(4) = 1
Substitution: 1 + 3 = 4
Examples
1. 7(4 – 3) – 1 + 5 ∙
1
5
7
2. 2 · 3 + (4 · 2 – 8)
6
1
4
3.
4
12 − 8 + 3 15 ÷ 5 − 2
A. 4
B. 5
C. 1
D. 0
Word Problem # 1
HORSEBACK RIDING Myra made a
list of trail lengths to find the
total miles she rode. Find the
total miles Myraa rode her horse.
Bent Tree
4.25
Knob Hill
+
6.50
Meadowrun
+
9.00
Answer: Myra rode 27.5 miles on the trails.
Pinehurst
+
7.75
Word Problem #2
TRANSPORTATION Darlene rode
the city train from the Winchester
Street Station to the airport. How
far did she travel on the train?
Practice
• Page 19 #1-8
You do not have to write property names!!
Homework
• Pages 19-20 #10-36 even
You do not have to write property names!!