2. Lesson 2-1 Warm-Up

3. Properties of Numbers (2-1)
What are all of the properties of real numbers?

4. Properties of Numbers
(2-1)

5. You can use the Associative Property of Addition to find the total
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) = = 52 Add 2 and 8 first.
(42 + 2) + 8 = = 52 Add 42 and 2 first.
Carlos’s total cost was $52.

6. Name each property shown.
Properties of Numbers
LESSON 2-1
Additional Examples
Name each property shown.
a. 17 + x + 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.  ( ) + 4 = (26 + 4)
Associative Property of Addition

7. 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 Commutative Property of Addition
= 6 + (81 + 9) Associative Property of Addition
= Parenthesis (PEMDAS)
= Add. (PEMDAS)

8. Use mental math to simplify (48 + 7) + 2.
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).
= Work within grouping symbols.
= 57 Add.

9. = 0.65 + 0.45 + 1.55 Use the Commutative Property of Addition.
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.
= Use the Commutative Property of Addition.
= ( ) Use the Associative Property of Addition.
= Work within grouping symbols.
= Add.
The cost of the school supplies is $2.65.

10. Use mental math to simplify (20 • 13) • 5.
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.

11. Name each property shown. 1. d  1 = d
Properties of Numbers
LESSON 2-1
Lesson Quiz
Name each property shown.
1. d  1 = d
(2 + 5) = (3 + 2) + 5
3. f  g = g  f
4. Simplify using mental math
Identity Property of Multiplication
Associative Property of Addition
Commutative Property of Multiplication
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