Solving Proportions with Algebraic Expressions A review of the cross-products property and the distributive property.

Slides:

Advertisements

Similar presentations

Algebra I B. MacDonald.  Standard form ax 2 + bx + c  a, b, c are real numbers.

Advertisements

Bell Work Simplify the expression: 1. 2(x +4) 2. 4x + 3y – x + 2y 3. 3(x – 6) x Answers: 2x+ 8 3x + 5y 11x – 14.

Equation Race Set 2 Distributive Property Solve your equation then add together your individual answers to get the final answer.

Common Core Standard 7.EE.1

Algebra I Concept Test # 2 – Equations, Inequalities and A.V.

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

Algebraic Expressions Objectives: 1)To evaluate algebraic expressions 2)To simplify algebraic expressions.

3-1 The Distributive Property

Distributive Property O To distribute and get rid of the parenthesis, simply multiply the number on the outside by the terms on the inside of the parenthesis.

Algebra 1 Chapter 1 Section Properties of Real Numbers The commutative and associate properties of addition and multiplication allow you to rearrange.

Algebraic proof Chapter 2 Section 6.

Distributive Property. The property that states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and.

Geometric and Arithmetic Means

Algebra 1 Ch.10 Notes Page 81 P Factoring to Solve Quadratic Equations.

 Geometric mean of any n numbers is:  Find the geometric mean of the following list of numbers. A. 4, 6 B. 3, 5, 9 C. 4, 8, 10, 12.

1-4: Properties of Equality and Algebraic Proofs Unit 1: Functions English Casbarro.

Operations on rational numbers

Find the total area of the rectangles using two different expressions 5 ft 10 ft+ 4 ft 5 ft.

PROPERTIES OF REAL NUMBERS. COMMUTATIVE PROPERTY OF ADDITION What it means We can add numbers in any order Numeric Example Algebraic Example

Simplifying Algebraic Expressions. 1. Evaluate each expression using the given values of the variables (similar to p.72 #37-49)

4 x 53 =4(50 + 3) =(4 x 50) + (4 x 3) = =212 Warm-up 4 x 27 =4(20 +7) =4(20) +4(7) = =108 Explain what is happening in each of these boxes,

Do Now 10/2/09 Take out HW from last night. Take out HW from last night. Text p.81, #10-21 all, #33-35 all Text p.81, #10-21 all, #33-35 all Copy HW in.

Objective- To use the distributive property to simplify variable expressions. Distributive Property a(b + c) = ab + ac or a(b - c) = ab - ac Order of OperationsDistributive.

1.5 The Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac (b + c)a = ba + ca a(b – c)=ab – ac (b – c)a = ba – ca For example: 3(2 +

Problem Solving in geom. w/ proportions. Proportion Properties If then If then.

ALGEBRA READINESS LESSON 1-6 Warm Up Lesson 1-6 Warm Up.

1 Math I can create equivalent expressions. Using the Distributive Property.

Chapter 1 Section 4 Distributive Property. Symbols: For any numbers a, b, c, a(b + c) = ab + ac and a(b - c) = ab – ac. Numbers: 2(5 + 3) = (2 ∙ 5) +

Unit 4 Review!. 1. Write the expression Sum of 9 and z.

9.3 Altitude-On-Hypotenuse Theorems (a.k.a Geometry Mean)

PROPERTIES USED IN ALGEBRA. What are they? ■Commutative Property ■Associative Property ■Identity Property ■Distributive Property ■Inverse Property.

Algebra 1 Section 2.6 Use the distributive property Combine similar terms Note: 7(105) = 735 Also 7(100+5) 7(100) + 7(5) = 735 3(x+2) 3x + 3(2)

Factor: 1. 2x 2 – 3x x 2 - 8x x 2 – 10x – 20.

5.5 Triangle Inequality. Objectives: Use the Triangle Inequality.

Before 10.7 Review of the Distributive Property.

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Write an expression which represents the perimeter of the rectangle?

Distributive Property

a(b + c) = ab + ac or a(b - c) = ab - ac Order of Operations

Solve the following equations: 6(4+8) −10 9−10 −10×9− −10 ×10

Properties of Real Numbers

2.5 Algebraic Proof Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction.

7.1 The Distributive Property

Geometric Model for Distributive Property

1.4 Basic Rules of Algebra.

THE DISTRIBUTIVE PROPERTY: Factoring the Expression

2.4 Algebraic Reasoning.

Equivalent Linear Expressions

a(b + c) = ab + ac Order of Operations Distributive Property 6(3 + 5)

·Like a rectangle but slanted ·Can't use slanted lines for area

The Distributive Property

Simplifying Algebraic Expressions

Multiplying Polynomials Using Algebra Tiles

King of the Mountain.

1.5 The Distribute Property of Multiplication over Addition

Evaluating expressions and Properties of operations

1.5 Distributing and Factoring

a(b + c) = ab + ac Order of Operations Distributive Property 6(3 + 5)

The Distributive Property Guided Notes

2-5 (Part I) Applying the Distributive Property

Learn to combine like terms in an expression.

Do Now: Simplify the algebraic expression 16y6 + 4y4 – 13y

Lesson 1.7 Distributive Property

Exercise Find the following products mentally. 5(20) 100 5(7) 35 5(27)

Distributive Property

Warm Up Simplify      20  2 3.

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Using the Distributive Property to Simplify Algebraic Expressions

Properties of Numbers Review Problems.

Presentation transcript:

Solving Proportions with Algebraic Expressions A review of the cross-products property and the distributive property

The Cross-Products Property

The Distributive Property What is the distributive property? a(b + c) = ab + ac HERE is the PROOF:

The Distributive Property For this one we will use a geometric proof Begin with: a(b + c) Create a rectangle with lengths a, b, c similar to the following: b + c a

The Distributive Property a(b + c) Find the Area of each piece of the rectangle: b + c aab ac

The Distributive Property a(b + c) Add the Areas to Find the Answer: ab + ac SO… a(b + c) = ab + ac b + c aab ac

Putting it All Together

Example 2