Transcript Properties of Numbers

PRE-ALGEBRA
Lesson 2-1 Warm-Up
PRE-ALGEBRA
Properties of Numbers
(2-1)
What are all of the
properties of real
numbers?
PRE-ALGEBRA
Properties of Numbers
(2-1)
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Additional Examples
Carlos spent $42 on his golf game. He then
bought a bottle of water for $2 and a chef’s salad for $8.
What was the total cost for his golf game and meal?
You can use the Associative Property of Addition to find the total
cost in two different ways.
42 + (2 + 8) = 42 + 10 = 52 Add 2 and 8 first.
(42 + 2) + 8 = 44 + 8 = 52 Add 42 and 2 first.
Carlos’s total cost was $52.
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Additional Examples
Name each property shown.
a. 17 + x + 3 = 17 + 3 + x
Commutative Property of Addition
b. (36  2)10 = 36(2  10)
Associative Property of Multiplication
c. km = km • 1
Identity Property of Multiplication
d. (103 + 26) + 4 = 103 + (26 + 4)
Associative Property of Addition
PRE-ALGEBRA
Properties of Numbers
(2-1)
How can you use
mental math to solve
problems?
To do complex problems mentally (in your head), rearrange the numbers
into problems that are easier to compute mentally using the properties of
numbers.
Example: Use mental math to simplify (81 + 6) + 9.
(81 + 6) + 9
= (6 + 81) + 9
= 6 + (81 + 9)
= 6 + 90
= 96
Commutative Property of Addition
Associative Property of Addition
Parenthesis (PEMDAS)
Add. (PEMDAS)
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Additional Examples
Use mental math to simplify (48 + 7) + 2.
(48 + 7) + 2
= (7 + 48) + 2 Use the Commutative Property of Addition (Switch Numbers).
= 7 + (48 + 2) Use the Associative Property of Addition (Switch Groupings).
= 7 + 50
Work within grouping symbols.
= 57
Add.
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Additional Examples
Suppose you buy school supplies costing $.45,
$.65, and $1.55. Use mental math to find the cost of
these supplies.
0.45 + 0.65 + 1.55
= 0.65 + 0.45 + 1.55
Use the Commutative Property of Addition.
= 0.65 + (0.45 + 1.55)
Use the Associative Property of Addition.
= 0.65 + 2.00
Work within grouping symbols.
= 2.65
Add.
The cost of the school supplies is $2.65.
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Additional Examples
Use mental math to simplify (20 • 13) • 5.
(20 • 13) • 5 = (13 • 20) • 5
Use the Commutative Property of
Multiplication.
= 13 • (20 • 5)
Use the Associative Property of
Multiplication.
= 13 • 100
Multiply within parentheses.
= 1,300
Multiply.
PRE-ALGEBRA
Properties of Numbers
LESSON 2-1
Lesson Quiz
Name each property shown.
1. d  1 = d
Identity Property of Multiplication
2. 3 + (2 + 5) = (3 + 2) + 5
Associative Property of Addition
3. f  g = g  f
Commutative Property of Multiplication
4. Simplify using mental math. 38 + 45 + 102
185
PRE-ALGEBRA