Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Homework # 7 – Word Problems pg 92 # 51 An investor purchases 50 shares of a stock at $3.50 per share. The next day, the change in value of a share of the stock is -$0.25. What is the total value of the shares the next day?

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Find the total areas of the two rectangles modeled below. Example # 1 7 units Total Area of the Rectangles = Area # 1 + Area # 2 x units 7 units 3 units Rectangle # 1 Rectangle # 2 Area of Rectangle = Length * Width Area # 1 = Length * Width Area # 1 = 7 units * x units Area # 1 = 7x units Area # 2 = Length * Width Area # 2 = 7 units * 3 units Area # 2 = 21 units Total Area of the Rectangles = 7x units + 21 units Total Area of the Rectangles = 7x + 21 units

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Find the area of the rectangle modeled below. Example # 1 (con’t) The Distributive Property allows you to find the product of a number with a sum/difference expression. x + 3 units 7 units Rectangle Area of Rectangle = Length * Width Area of Rectangle = 7 units *( x + 3 ) units Area of Rectangle = ((7 * x) + (7 * 3))units Area of Rectangle = 7x + 21 units Note: Thus; Total Area of the Rectangles = Area of Rectangle Total Area of the Rectangles = 7x + 21 units

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property 4(x-2) (3-5)6 6(3-5) 4(x+5) (3+5)4 4(3+5) Given Examples = 4(x) - 4(2) = (3)6 - (5)6 = 6(3) - 6(5) = 4(x) + 4(5) = (3)4 + (5)4 = 4(3) + 4(5) Distributive Step = = -12a(b - c) = ab - acThe product of a and (b - c) = = -12(b - c)a = ba - ca = 4x + 20 = 4x - 8 = = 32(b + c)a = ba + ca = = 32a(b + c) = ab + acThe product of a and (b + c) AnswerAlgebraWords Distributive Property

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Example # 2 Use the distributive property to write an equivalent expression. a) (y – 2) * (-4) (y)*(-4) – (2)*(-4) -4y – (-8) -4y – (-8) -4y + 8 Distribute -4 Multiply Add the opposite of - 8 Simplified Expression b) -5x * (4 - x) (-5x)*(4) – (-5x)*(x) -20x – (-5x 2 ) -20x – (-5x 2 ) -20x + 5x 2 Distribute -5x Multiply Add the opposite of -5x 2 Simplified Expression c) -(3y – 9) (-1)*(3y) – (-1)*(9) -3y – (-9) -3y – (-9) -3y + 9 Distribute -1 Multiply Add the opposite of - 9 Simplified Expression

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Coefficient – the number part of a term with a variable part Terms – the parts of the expression that are added together Constant – the number part of expression that does not contain a variable Like Terms – are terms that have the same variable parts Example # 3 Identify the terms, like terms, coefficients, and constant terms of the following expression a) -2x – 8 + 6x + 5 c) 6 - 5x + 3y + 6 b) 3y + 6 – 8y – 2 Constant Terms: -8, +5 Constant Terms: 6, -2 Constant Terms: 6, 6 Coefficients: -2, +6Like Terms: -2x, 6x; -8, +5; Like Terms: 3y, -8y; +6, -2Coefficients: 3, -8 Coefficients: -5, 3Like Terms: 6, 6;

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property PROBLEM SOLVING PLAN READ AND UNDERSTAND Read the Problem CAREFULLY!!! STEP 1 : Identify Variables and Constants. What is the problem asking? ORGANIZE YOUR THOUGHTS Formulate an Approach. STEP 2 : Make an equation, inequality or expression. SOLVE THE PROBLEM Evaluate the equation, inequality or expression STEP 3 : CHECK YOUR WORK DOES IT MAKES SENSE!!! STEP 4 :

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Example # 3 You are making curtains by alternating strips of solid colored fabric and patterned fabric. The solid colored fabric costs $0.99 per strip and the patterned fabric costs $1.25 per strip. You need 7 strips for one curtain. Find the total cost if you use 3 solid colored strips. Write a verbal model. Multiply C = ($0.99) * S + ($1.25) * (7 – S) Total Cost for Curtain w/ 3 Solid = Colored Strips (dollars) Cost for Solid Colored Strips (dollars per strips) Cost for + Patterned Colored Strips (dollars per strips) Number of * Solid Colored Strips (strips) Combine Like Terms Distribute $1.25 Simplified Equation Number of * Patterned Colored Strips (strips) C = ($0.99)* S + ($1.25) * (7 – S) Write an Equation. C = $0.99S + ($1.25)(7) - ($1.25)(S) C = $0.99S + $ $1.25S C = $ $0.26S

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Example # 3 (con’t) You are making curtains by alternating strips of solid colored fabric and patterned fabric. The solid colored fabric costs $0.99 per strip and the patterned fabric costs $1.25 per strip. You need 7 strips for one curtain. Find the total cost if you use 3 solid colored strips. Add Multiply Find the Total Cost (C) when the number of colored strips (S) = 3. C = $ $0.78 C = $7.97 C = $ $0.26(3) The total cost if you use 3 solid colored fabric strips to make a curtain is $ Substitute

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.6 – Divide Real Numbers Inverse Property of Multiplication The product of a nonzero number and its multiplicative inverse is 1. Example # 4 Division Rule To divide a number a by a nonzero number b, multiply a by the multiplicative inverse of b. a)b) The Sign of a Quotient - The quotient of two real numbers with the same sign is positive. The quotient of two real numbers with different signs is negative. The quotient of 0 and any nonzero real numbers is 0.

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.6 – Divide Real Numbers Example # 5 Simplify the following expression. a) = = = = Apply the division rule Use the Distributive Property Simplify Rewrite the fraction as division

Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Homework # 8 pg 99 # 3 – 42 mult. of 3; # 53 pg 106 # 9 – 23 odd; # 33 – 43 odd Section 2.5, 2.6