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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 Example # 1 Find the total areas of the two rectangles modeled below. Area of Rectangle = Length * Width Area # 1 = Length * Width Area # 1 = 7 units * x units Area # 1 = 7x units Rectangle #1 7 units Rectangle 7 units #2 Area # 2 = Length * Width Area # 2 = 7 units * 3 units Area # 2 = 21 units x units Total Area of the Rectangles = Area # 1 + Area # 2 Total Area of the Rectangles = 7x units + 21 units Total Area of the Rectangles = 7x + 21 units 3 units Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Example # 1 (con’t) Find the area of the rectangle modeled below. Rectangle Area of Rectangle = Length * Width Area of Rectangle = Length * Width Area of Rectangle = 7 units *( x + 3 ) units 7 units Area of Rectangle = ((7 * x) + (7 * 3))units Area of Rectangle = 7x + 21 units Note: Total Area of the Rectangles = 7x + 21 units x + 3 units Thus; Total Area of the Rectangles = Area of Rectangle The Distributive Property allows you to find the product of a number with a sum/difference expression. Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Examples Distributive Property Given Distributive Step The product of a and (b + c) a(b + c) = ab + ac 4(3+5) = 4(3) + 4(5) = 12 + 20 = 32 (b + c)a = ba + ca (3+5)4 = (3)4 + (5)4 = 12 + 20 = 32 4(x+5) = 4(x) + 4(5) = 4x + 20 a(b - c) = ab - ac 6(3-5) = 6(3) - 6(5) = 18 - 30 = -12 (b - c)a = ba - ca (3-5)6 = (3)6 - (5)6 = 18 - 30 = -12 4(x-2) = 4(x) - 4(2) = 4x - 8 Words The product of a and (b - c) Algebra Answer 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) Distribute -4 (y)*(-4) – (2)*(-4) Multiply b) -5x * (4 - x) (-5x)*(4) – (-5x)*(x) Multiply -4y – (-8) Add the opposite of - 8 -20x – (-5x2) -4y + 8 Simplified Expression c) -(3y – 9) Distribute -5x -20x + 5x2 Distribute -1 (-1)*(3y) – (-1)*(9) Multiply -3y – (-9) Add the opposite of - 9 -3y + 9 Simplified Expression Add the opposite of -5x2 Simplified Expression Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property Terms – the parts of the expression that are added together Coefficient – the number part of a term with a variable part 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 Like Terms: -2x, 6x; -8, +5; Coefficients: -2, +6 Constant Terms: -8, +5 Coefficients: 3, -8 Constant Terms: 6, -2 Coefficients: -5, 3 Constant Terms: 6, 6 b) 3y + 6 – 8y – 2 Like Terms: 3y, -8y; +6, -2 c) 6 - 5x + 3y + 6 Like Terms: 6, 6; Chapter 2 – Properties of Real Numbers Algebra I A - Meeting 9 Section 2.5 – Apply the Distributive Property PROBLEM SOLVING PLAN STEP 1 : READ AND UNDERSTAND Read the Problem CAREFULLY!!! Identify Variables and Constants. What is the problem asking? STEP 2 : ORGANIZE YOUR THOUGHTS Formulate an Approach. Make an equation, inequality or expression. STEP 3 : SOLVE THE PROBLEM Evaluate the equation, inequality or expression STEP 4 : CHECK YOUR WORK DOES IT MAKES SENSE!!! 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. Total Cost for Curtain Cost for w/ 3 Solid = Solid Colored Colored Strips Strips Number of Cost for Number of * Solid Colored + Patterned Colored * Patterned Colored Strips Strips Strips (strips) (dollars per strips) (strips) (dollars per strips) (dollars) Write an Equation. C = ($0.99) * S + ($1.25) * (7 – S) C = ($0.99)* S + ($1.25) * (7 – S) Distribute $1.25 C = $0.99S + ($1.25)(7) - ($1.25)(S) Multiply C = $0.99S + $8.75 - $1.25S Combine Like Terms C = $8.75 - $0.26S Simplified Equation 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. Find the Total Cost (C) when the number of colored strips (S) = 3. Substitute C = $8.75 - $0.26(3) Multiply C = $8.75 - $0.78 Add C = $7.97 The total cost if you use 3 solid colored fabric strips to make a curtain is $ 7.97. 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. a 1 1 a 1, a 0 a a Division Rule To divide a number a by a nonzero number b, multiply a by the multiplicative inverse of b. 1 a b a Example # 4 a) 8 1 1 8 b ,b 0 b) 5 2 5 1 2 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 Section 2.6 – Divide Real Numbers Example # 5 Simplify the following expression. a) 40 x 32 8 Rewrite the fraction as division = Apply the division rule = Use the Distributive Property = Simplify = Algebra I A - Meeting 9 Chapter 2 – Properties of Real Numbers Section 2.5, 2.6 Homework # 8 pg 99 # 3 – 42 mult. of 3; # 53 pg 106 # 9 – 23 odd; # 33 – 43 odd Algebra I A - Meeting 9