CHAPTER 11 – PART A Lesson’s Covered: QUIZ COVERING QUIZ COVERING Part A TEST

Algebra I – Chapter 11 Daily Warm-Up Factor the Trinomial 1. y² + 5y - 14 Solve the Quadratic Equation by Factoring 2. x² - 9x = -14

11.1 Ratio and Proportion Objectives: 1.Write and solve proportions 2.Use proportions in real life

The steepness of a hill can be written as the ratio of its height to its horizontal extent. Ratios can be expressed as follows: 2 to 3 2:3 2/3 A ratio is a comparison of two quantities of the same kind, expressed in the same units.

A proportion is an equation stating that 2 ratios are equal. Read: “1 is to 3 as 4 is to 12” Read: is a proportion 

Cross Product Property: The product of the extremes equals the product of the means. Apply the cross product property to: bcad  6x5y  303a  4362  Extremes Means a = ?

Solve the proportions: 12 w  2w = 24 4y = = 2t ² 25 = t² 2 9 y  5 t 

Solve the proportions:

YOUR TURN-Solve the proportions:

Extraneous solution – solution that doesn’t satisfy the original equation. Why not ±3? 2(y ² - 9) = (y + 3)(y – 3) 2y² - 18 = y² - 9 y² - 9 = 0 (y + 3)(y – 3) = 0 y = ? Remember to check in original equation!!

Extraneous solution – solution that doesn’t satisfy the original equation. YOU TRY-Remember to check for Extraneous Solutions!

Using Proportions in Real Life You want to make a scale model of a parade float. The float is 5.5 feet long and 10 feet high. Your model will be 14 inches high. How long should it be?

Algebra I – L 11.1 What is present in every paint bucket but absent in every translucent bucket? Clue: it is not paint. Tonight’s Homework: Pages #’s 17-18, 27-28, 30-31, 44

Algebra I – Chapter 11 Daily Warm-Up

11.2 Percents Goal: Use equations to solve percent problems Use percents in real-life problems

What is 50% of 90? Percent Equation: Percent Proportion: a = p * ba/b = p/100 a = b = p = of =. (multiplication) % = decimal (move 2 to the left) – For Equation ONLY! Is = “=“

Let’s Solve for a, p, or b? What is 150% of $200? 9.6 is 12% of what number? 131 is what % of 255?

Your Turn. Solve each % Problem. 18 is what percent of 60? 52 is 12.5% of what number? What distance is 24% of 710 miles? $4 is 2.5% of what number? 2 is what percent of 40 feet? 9 people is what percent of 60 people? 85% of 300 is what number?

The graph shows the results of a poll of student taken to find out the average amount of time spent on various activities in a 24 hour period. How many hours on average spent sleeping? How many hours watching TV?

Algebra I – L I am a 6 letter word. Letters spell out a drink. Letters spell out a fruit. Letters spell out a pet. Letters spell out a pest, which often gets eaten by What am I? Tonight’s Homework: Page 653 #’s 10-20, 33

Algebra I – Chapter 11 Daily Warm-Up  What number is 54% of $88?  631 feet is what percent of 1,281 feet?

11.4 Simplifying Rational Expressions Goals: 1. Simplify a rational expression 2. Use rational expressions to find geometric probability

Rational number = a number that can be written as a quotient of 2 integers (fraction)

Rational expressions = an expression number that can be written as a fraction of 2 nonzero polynomials

Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

= = What values for x would make these expressions undefined? Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

= = x ≠ 0, 1/2 What values for x would make these expressions undefined? Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

Simplify Rational Expressions: 1.Factor out a GCF, if possible 2.Factor if it is quadratic, if possible 3.Reduce the numerical part, if possible 4.Cancel out common factors (blocks)

Algebra I – L 11.4 There were four brothers who were born in this world together. One runs but is never weary, One eats but is never full, One drinks but is never thirsty, One sings a song that is never good. Who are they? Tonight’s Homework: Page 667 #’s 9-11, 18-20, 25-26

Algebra I – Chapter 11 Daily Warm-Up

11.5 Multiplying and Dividing Rational Expressions Goals: Multiply and divide rational expressions Use rational expressions in real-life models

Multiply fractions: Divide fractions: Keep Change Flip

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks)

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks) (2x-3)(x+1) 3)(2x 3x2x 1 2    1

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks)

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks)

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks) = 2n 5 +n 2n 2-n  = n+5 2n keep change flip

Multiply/Divide Rational Expressions: 1.If Division, change to Multiplication 2.GCF & factor quadratics if possible 3.Cancel all common factors (blocks) 4)-(x 5x 20x-5x²   =

Now you try:

Algebra I – L 11.5 Tonight’s Homework: Page 673 #’s 12, 15, 18, 22, 32 1.Remove six letters from this sequence to reveal a familiar English word. BSAINXLEATNTEARS 1.If you drop me I'm sure to crack but give me a smile and I'll always smile back

CHAPTER 11 – PART B Lesson’s Covered: QUIZ COVERING Part B TEST

11-6 Adding and Subtracting Rational Expressions Goal: Add & subtract rational expressions with like and unlike denominators.

Vocabulary  LCD – Least common denominator is the least common multiple of the denominators of two or more fractions.

Adding and Subtracting with Like Denominators  Let a, b, and c be polynomials, with c ≠0.  To add, add numerators: a + b = a + b c c c  To subtract, subtract the numerators. a – b = a – b c c c

Ex 1 – Common Denominators 7 + 2x -7 = 7 +(2x – 7) = 2x = 2x 2x 5 - 2m = 5 – 2m 3m – 4 3m – 4 3m - 4 1

Now you try: 1) 5 + x – 6 = 3x 2) 9 - 4n = 2n – 1 2n - 1

Ex 2 – Common Denominators 3x - x + 1 = 3x – ( x + 1) 2x² + 3x - 2 2x² + 3x - 2 2x² + 3x – 2 = 2x – 1 Factor and divide out common factors (2x – 1) ( x + 2) = 1 x + 2 Simplified form

Add or Subtract and Simplify

Finding the Least Common Denominator (LCD) Step 1. Factor each denominator completely. Step 2. The LCD is the product of all unique factors each raised to the greatest power that appears in any factored denominator.

Adding or Subtracting Rational Expressions with Different Denominators Step 1. Find the LCD. Step 2. Rewrite each rational expression as an equivalent rational expression whose denominator is the Step 1 LCD. Step 3. Add or Subtract numerators. Write result over LCD. Step 4. Simplify the resulting rational expression.

Example 3 1. Find least common denominator 2. Rewrite fractions as LCD fractions 3. Add or Subtract 4. Reduce x 6x²

Example 4 - TOGETHER x = x - 2 x + 2

YOU TRY… Add/Subtract and Simplify 1) x + 3 x – 3 2) x – 1 x + 4

Algebra I – L 11.6 What starts with T ends with T and is full of T? Tonight’s Homework: Page 679 #’s 10-11, 18-19, 28

Algebra I – Chapter 11 Daily Warm-Up x + 3 x – 3

Lesson 11.7 Dividing Polynomials 1. Divide a polynomial by a monomial or by a binomial factor. 2. Use polynomial long division.

Dividing a Polynomial by a Monomial LONG DIVISION REVIEW Divide 5103 by 7 using long division.

Dividing a Polynomial by a Monomial Divide 12x² + 15x – 18 by 3x

Dividing a Polynomial by a Monomial Divide 12x² – 20x + 8 by 4x. Divide 9x³ – 27x² + 21x – 18 by 3x².

Long Division  Divide 270 by 20 ) (20)=20 Subtract and bring down next digit (20)=60 60 Subtract. The remainder is Dividend Divisor 310/20 The quotient is 13 ½. remainder divisor

Polynomial Long Division  Put dividend in standard form (with spacers) and into the division box  Multiply the divisor so the first terms are exact  Draw the line, change the sign, and combine  Bring down next term  With no more terms, put the remainder in a fraction with the divisor.

Polynomial Long Division Divide x² - 3x + 5 by x + 2.

YOU TRY - Polynomial Division Divide x² + 2x + 4 by x – 1.

YOU TRY - Polynomial Division Divide 5n² + 2 by n + 1.

YOU TRY - Polynomial Division Divide x – x² by 3x + 1.

Algebra I – L 11.7 I can easily be broken, yet, no one touches me. What am I? Tonight’s Homework: Pages #’s 18-20, 27-29, 48

Algebra I – Chapter 11 Daily Warm-Up Divide 6x³ – 24x² + 20x – 10 by 2x Divide x² - 3x + 2 by x – 2

11.8 Rational Equations Goal: Solve rational equations.

A rational equation is an equation that contains rational expressions. Cross Multiplying - Can be used only for equations with a single fraction on each side. 4-x 4 3 x  Now you try:

Multiply by the LCD to get rid of fractions. Then solve.

You may need to factor first to find the LCD. Then solve as before. (y+4)(y-3) LCD=(y+4)(y-3)

YOU TRY…

YOU TRY…CHALLENGE!

Summary Cross Multiply Multiply by the LCD Factor and then multiply by the LCD

Algebra I – L 11.8 What is the animal who's name is three letters long, take away the first letter and you have bigger animal? Tonight’s Homework: Page 694 #’s 14-15, 21, 28, 33