Properties and Mental Math Warm Up Find each

Properties and Mental Math Warm Up Find each sum or product. 1. 2. 3. 4. 5. 6. 17 + 15 32 29 + 39 68 8(24) 192 7(12) 84 3(91) 273 6(15) 90

Properties and Mental Math Learn to use number properties to compute mentally.

Properties and Mental Math Vocabulary Commutative Property Associative Property Distributive Property

Properties and Mental Math Mental math means “doing math in your head. ” Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

Properties and Mental Math COMMUTATIVE PROPERTY (Ordering) Words You can add or multiply numbers in any order. Numbers 18 + 9 = 9 + 18 15 2 = 2 15

Properties and Mental Math ASSOCIATIVE PROPERTY (Grouping) Words When you are only adding or only multiplying, you can group any of the numbers together. Numbers (17 + 2) + 9 = 17 + (2 + 9) (12 2) 4 = 12 (2 4)

Properties and Mental Math Caution! The Commutative and Associative Properties do not apply to subtraction or division.

Properties and Mental Math Additional Example 1 A: Using Properties to Add and Multiply Whole Numbers Simplify 17 + 5 + 3 + 15 Look for sums that are multiples of 10 17 + 3 + 5 + 15 Use the Commutative Property. Use the Associative (17 + 3) + (5 + 15) Property to make groups of compatible numbers. 20 + 20 40 Use mental math to add.

Properties and Mental Math Additional Example 1 B: Using Properties to Add and Multiply Whole Numbers Simplify 4 13 5 Look for products that are multiples of 10 13 4 5 Use the Commutative Property. 13 (4 5) Use the Associative Property to group compatible numbers. 13 20 Use mental math to multiply. 260

Properties and Mental Math Helpful Hint The expressions in each row of example 1 B are equivalent because they have the same value.

Properties and Mental Math Check It Out: Example 1 A Simplify 12 + 5 + 8 + 5 Look for sums that are multiples of 10 12 + 8 + 5 Use the Commutative Property. (12 + 8) + (5 + 5) Use the Associative Property to make groups of compatible numbers. 20 + 10 30 Use mental math to add.

Properties and Mental Math Check It Out: Example 1 B Simplify 8 3 5. 8 3 5 Look for products that are multiples of 10. 3 8 5 Use the Commutative Property. 3 (8 5) Use the Associative Property to group compatible numbers. 3 40 Use mental math to multiply. 120

Properties and Mental Math DISTRIBUTIVE PROPERTY Words Numbers To multiply a number by a sum, multiply by 6 (10 + 4) = (6 10) + (6 4) each number in the = 60 + 24 sum and then add. = 84

Properties and Mental Math When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

Properties and Mental Math Additional Example 2 A: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6 35 = 6 (30 + 5) “Break apart” 35 into 30 + 5. = (6 30) + (6 5) Use the Distributive Property. = Use mental math to multiply. = 180 + 210 30 Use mental math to add.

Properties and Mental Math Additional Example 2 B: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9 87 = 9 (80 + 7) “Break apart” 87 into 80 + 7. = (9 80) + (9 7) Use the Distributive Property. = Use mental math to multiply. = 720 + 783 63 Use mental math to add.

Properties and Mental Math Check It Out: Example 2 A Use the Distributive Property to find the product. 4 27 = 4 (20 + 7) “Break apart” 27 into 20 + 7. = (4 20) + (4 7) Use the Distributive Property. = Use mental math to multiply. = 80 + 108 28 Use mental math to add.

Properties and Mental Math Check It Out: Example 2 B Use the Distributive Property to find the product. 6 43 = 6 (40 + 3) “Break apart” 43 into 40 + 3. = (6 40) + (6 3) Use the Distributive Property. = Use mental math to multiply. = 240 + 258 18 Use mental math to add.

Properties and Mental Math Lesson Quizzes Standard Lesson Quiz for Student Response Systems

Properties and Mental Math Lesson Quiz Simplify. 1. 18 + 24 + 2 + 6 50 2. 10 5 3 150 3. 13 + 42 + 7 + 8 70 Use the Distributive Property to find each product. 4. 8 12 96 5. 6 15 90 6. 5 34 170 7. 3 71 213

Properties and Mental Math Lesson Quiz for Student Response Systems 1. Evaluate 16 + 23 + 4 + 7. A. 50 B. 40 C. 30 D. 20

Properties and Mental Math Lesson Quiz for Student Response Systems 2. Evaluate 3 7 10. A. 140 B. 170 C. 190 D. 210

Properties and Mental Math Lesson Quiz for Student Response Systems 3. Evaluate 15 + 56 + 5 + 4. A. 86 B. 80 C. 77 D. 70

Properties and Mental Math Lesson Quiz for Student Response Systems 4. Use the Distributive Property to find the product. 7 15 A. 135 B. 125 C. 115 D. 105

Properties and Mental Math Lesson Quiz for Student Response Systems 5. Use the Distributive Property to find the product. 4 73 A. 292 B. 282 C. 272 D. 262