Click the mouse button or press the Space Bar to display the answers. Transparency 1

Splash Screen

Objective Use the Commutative, Associative, Identity, and Distributive Properties Example 1-5b

Vocabulary None Example 1-5b

Properties Property Algebra Arithmetic Commutative a + b = b + a 6 + 1 = 1 + 6   a · b = b · a 7 · 3 = 3 · 7 Associative a + (b + c) = (a + b) + c 2 + (3 + 8) = (2 + 3) + 8 a · (b · c) = (a · b) · c 3 · (4 · 5) = (3 · 4) · 5 Distributive a(b + c) = ab + ac 4(6 + 2) = 4(6) + 4(2) a(b - c) = ab - ac 3(7 - 5) = 3(7) - 3(5) Identity Additive a + 0 = a 9 + 0 = 9   Multiplicative a · 1 = a 5 · 1 = 5 Transitive if a = b and b = c, then a = c If 2 + 4 = 6 and 6 = 3 · 2, then 2 + 4 = 3 · 2 (Change position of numbers) (Regroup numbers) (Distribute numbers) Example 1-5b

Example 1 Use the Distributive Property Example 2 Apply the Distributive Property Example 3 Identify Properties Example 4 Identify Properties Example 5 Apply Properties Lesson 1 Contents

Find 6  43 using the Distributive Property Write the problem 6  43 6 (40 + 3) Write 43 as Bring down 6 6(40) + 6(3) Use the Distributive Property Distribute the 6 to the 40 Bring down + Distribute the 6 to the 3 1/4 Example 1-1a

Find 6  43 using the Distributive Property Follow Order of Operations P E MD AS 6  43 6 (40 + 3) Multiply from left to right 6(40) + 6(3) Bring down + 240 + 18 Add Answer: 258 1/4 Example 1-1a

Find 7  33 using the Distributive Property. Answer: 231 1/4 Example 1-1b

Identify the property shown by the equation 3 + 2 = 2 + 3 Write the problem Identify what is happening to the numbers Answer: Begins with 3 + 2 Commutative Property Ends with 2 + 3 of Addition Changed position of numbers Identify property Identify process 2/4 Example 1-3a

Identify the property shown by the equation 9  6 = 6  9 Answer: Commutative Property of Multiplication 2/4 Example 1-3b

Identify the property shown by the equation (13  3)  4 = 13  (3  4) Write the problem (13  3)  4 = 13  (3  4) Identify what is happening to the numbers Answer: Begins with (13  3)  4 Associative Property Ends with 13  (3  4) of Multiplication Regrouping numbers Identify property Identify process 3/4 Example 1-4a

Identify the property shown by the equation (10 + 7) + 4 = 10 + (7 + 4) Answer: Associative Property of Addition 3/4 Example 1-4b

Now use the Associative Property by using parenthesis around the 2  4 Find 12  2  4 using the Commutative Property and the Associative Property Write the problem 12  2  4 Since you can easily multiply 2 and 4, change the order by using the Commutative Property 2  4  12 (2  4)  12 Now use the Associative Property by using parenthesis around the 2  4 4/4 Example 1-5a

Follow Order of Operations P E MD AS 12  2  4 Find 12  2  4 using the Commutative Property and the Associative Property Follow Order of Operations P E MD AS 12  2  4 2  4  12 Work inside parenthesis (2  4)  12 Multiply 8  12 Answer: 96 4/4 Example 1-5a

Find using the Commutative Property and Associative Property * Find using the Commutative Property and Associative Property Answer: 117 4/4 Example 1-5b

Assignment Lesson 9:1 Properties 19 - 42 All End of Lesson 1

Find the cost of 5 admissions and 5 meals. Then add. THEME PARKS Suppose admission to a theme park costs $35 per person and meals cost $20 per person. What is the cost for a family of 5 people? Find the cost of 5 admissions and 5 meals. Then add. cost of 5 admissions cost of 5 meals Answer: The total cost is $275. 2/5 Example 1-2a

BOWLING Suppose the cost of bowling three games at a local bowling alley is $6.50 and the cost of shoe rental is $1.50. What is the cost for a group of 6 friends to each rent a pair of shoes and bowl three games? Answer: $48 2/5 Example 1-2c