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

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Lesson 2-1 Warm-Up

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

Properties of Numbers (2-1)

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) = 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.

Name each property shown. 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

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 = 6 + 90 Parenthesis (PEMDAS) = 96 Add. (PEMDAS)

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). = 7 + 50 Work within grouping symbols. = 57 Add.

= 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. 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.

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.

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. 3 + (2 + 5) = (3 + 2) + 5 3. f  g = g  f 4. Simplify using mental math. 38 + 45 + 102 Identity Property of Multiplication Associative Property of Addition Commutative Property of Multiplication 185