Transcript 11-6 PPT
5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 1. 4 (x + 2) 2. 5 (2x + 7) 3. 2( x + 4) 4. 6(5 + 2 x) 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 1. 4 (x + 2) 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 1. 4 (x + 2) = 4x + 8 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 2. 5 (2x + 7) 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 2. 5 (2x + 7) = 10x + 35 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 3. 2( x + 4) 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 3. 2( x + 4) = 2x + 8 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 4. 6(5 + 2 x) 5 Minute Check Complete on the back of your homework. Use the Distributive Property to rewrite each algebraic expression. 4. 6(5 + 2 x) = 30 + 12x Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Inquiry Lab Work with a partner and complete page 494 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Inquiry Lab Work with a partner and complete page 294 Thursday, Nov 6 Lesson 6.6.7 Equivalent Expressions Equivalent Expressions Objective: To understand how to use properties to simplify expressions. Equivalent Expressions A term can be a single number or variable or numbers and variables multiplied together and separated by addition or subtraction. e.g. 4x + 4 This expression has 2 terms. Equivalent Expressions A coefficient is the numerical factor of a term that contains a variable. e.g. 4x + 4 In this expression there is only one term that has a variable and the coefficient is 4. Equivalent Expressions A term without a variable is called a constant. e.g. 4x + 4 Constant. Equivalent Expressions Like terms are terms that contain the same variable. Only like terms can be added or subtracted. e.g. 4x + 6 + 5x Like terms Equivalent Expressions To simplify an numeric or algebraic expression, use properties to write an equivalent expression that has no like terms and no parentheses. Numeric 3 + 3 = 2(3) or 6 Algebraic x + x = 2x Equivalent Expressions Simplify the expression 6(4x) Equivalent Expressions Simplify the expression 6(4x) According to the Associative Property if an expression has all multiplication or addition, we can remove the parenthesis. 6·4·x Can we perform any operation? Equivalent Expressions Simplify the expressions 6(4x) 24x Equivalent Expressions Simplify the expression 11(3x) Do this on your own. Equivalent Expressions Simplify the expression 11(3x) 33x Equivalent Expressions Simplify the expression x+x+x Do this on your own. Equivalent Expressions Simplify the expression x+x+x 3x When adding like terms, add the coefficients. Equivalent Expressions Simplify the expression 5x + 3x + 6x Do this on your own. Equivalent Expressions Simplify the expression 5x + 3x + 6x 14x Equivalent Expressions Simplify the expression (14y + x) + 22y Equivalent Expressions Simplify the expression (14y + x) + 22y According to the Associative Property if an expression has all multiplication or addition, we can remove the parenthesis. 14y + x + 22y Can we perform any operation? Equivalent Expressions Simplify the expression (14y + x) + 22y 36y + x Remember you can only add or subtract like terms. Equivalent Expressions Simplify the expression 3x + (9y + 2x) Do this on your own. Equivalent Expressions Simplify the expression 3x + (9y + 2x) 5x + 9y Equivalent Expressions Simplify the expression 4(2x + y) Do this on your own. Equivalent Expressions Simplify the expression 4(2x + y) 4 ·2x + 4 · y 8x + 4y Equivalent Expressions Simplify the expression 9(3x + 2y) Do this on your own. Equivalent Expressions Simplify the expression 9(3x + 2y) 9 ·3x + 9 · 2y 27x + 18y Equivalent Expressions Simplify the expression 4(3x + 7y) Do this on your own. Equivalent Expressions Simplify the expression 4(3x + 7y) 4 ·3x + 4 · 7y 12x + 28y Equivalent Expressions What is the sum of 4 and a number added to 13 as an expression? Do this on your own. Equivalent Expressions What is the sum of 4 and a number added to 13 as an expression? 4 + n + 13 17 + n Equivalent Expressions What is four sets of the sum a number and 6 as an expression? Equivalent Expressions What is four sets of the sum a number and 6 as an expression? 4( n + 6) 4n + 24 Equivalent Expressions A farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use a to represent the cost of each apple and p to represent the cost of each pear. Write and simplify an expression that represents the total cost of 5 baskets. What is in each group? Equivalent Expressions A farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use a to represent the cost of each apple and p to represent the cost of each pear. Write and simplify an expression that represents the total cost of 5 baskets. (3a + p) How many groups are there? Equivalent Expressions A farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use a to represent the cost of each apple and p to represent the cost of each pear. Write and simplify an expression that represents the total cost of 5 baskets. 5(3a + p) Can we simplify? Equivalent Expressions A farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use a to represent the cost of each apple and p to represent the cost of each pear. Write and simplify an expression that represents the total cost of 5 baskets. 5(3a + p) = 15a + 5p Equivalent Expressions The gift bag from Claire Cosmetics includes 5 bottles of nail polish and 2 tubes of lip gloss. Use p to represent the cost of each bottle of nail polish and g to represent the cost of each tube of lip gloss. Write and simplify an expression that represents the total cost of 8 gift bags. Do this on your own. Equivalent Expressions The gift bag from Claire Cosmetics includes 5 bottles of nail polish and 2 tubes of lip gloss. Use p to represent the cost of each bottle of nail polish and g to represent the cost of each tube of lip gloss. Write and simplify an expression that represents the total cost of 8 gift bags. 8(5p + 2g) = 40p + 16g Equivalent Expressions A fall candle gift set has 4 vanilla candles and 6 pumpkin spice candles. Use v to represent the cost of each vanilla candles and p to represent the cost of each pumpkin spice candle. Write and simplify an expression that represents the total cost of 4 sets. Do this on your own. Equivalent Expressions A fall candle gift set has 4 vanilla candles and 6 pumpkin spice candles. Use v to represent the cost of each vanilla candles and p to represent the cost of each pumpkin spice candle. Write and simplify an expression that represents the total cost of 4 sets. 4(4v + 6p) = 16v + 24p Equivalent Expressions Seven friends have similar cell phone plans. The price of each plan is $x. Three of the seven friends pay an extra $4 per month for unlimited texts. Write and simplify and expression that represents the total cost of the seven plans. Do this on your own. Equivalent Expressions Seven friends have similar cell phone plans. The price of each plan is $x. Three of the seven friends pay an extra $4 per month for unlimited texts. Write and simplify and expression that represents the total cost of the seven plans. 3(x + 4) + 4x = 3x + 12 + 4x = 7x + 12 Equivalent Expressions Mikayla bought five skirts at $x each. Three of the five skirts came with a matching top for an additional $9 each. Write and simplify an expression that represents the total cost of her purchase. Do this on your own. Equivalent Expressions Mikayla bought five skirts at $x each. Three of the five skirts came with a matching top for an additional $9 each. Write and simplify an expression that represents the total cost of her purchase. 3(x + 9) + 2x = 3x + 27 + 2x = 5x + 27 Equivalent Expressions Translate the verbal expression into an Simplify. 7x + 5(x + 3) + 4x – x - 2 Equivalent Expressions Translate the verbal expression into an Simplify. 7x + 5(x + 3) + 4x – x – 2 7x + 5x + 15 + 4x – x – 2 15x + 13 Equivalent Expressions Translate the verbal expression into an Simplify. 6 + 2(x – 8) + 3x – 11 + x Equivalent Expressions Translate the verbal expression into an Simplify. 6 + 2(x – 8) + 3x – 11 + x 6 + 2x – 16 + 3x – 11 + x 6x - 21 Equivalent Expressions Agenda Notes Homework – Homework Practice 6.6.7 Due Friday, Nov 7 Chapter 6.6 Test –Monday, Nov 10 Accum Rev 6 due Nov 10