Lesson 10-3 Operations with a Radical Expressions – We completed the homework problems for Lesson 10-3 Operations with Radical Expressions. Hudson had difficulty with most of these problems. I sent him a few problems to do which reviewed the concepts from Lesson 10-2 Simplifying Radical Expressions – We reviewed the Product Property of Square Roots and the Quotient Property of Square Roots. We will work on a practice test on Wednesday.
Lesson 11-8 Rational Equations – We practiced solving rational equations and simplifying rational expressions to prepare for a quiz tomorrow. We practiced adding and subtracting rational expressions with unlike denominators. Then we solved rational algebraic equations and determined the extraneous solutions.
Lesson 11-8 Rational Equations – We practiced solving rational equations. We completed homework where we used the cross product to solve rational expressions when both sides of the equation are single fractions. Then we practiced solving rational equations by multiplying each side of the equation by the LCD to eliminate fractions. Next, we practiced determining which solutions make the denominator of a rational expression zero.
Lesson 11-8 Rational Equations – We learned how to solve rational equations. We practiced using the cross product to solve rational expressions when both sides of the equation are single fractions. Then we learned how to solve rational equations by multiplying each side of the equation by the LCD to eliminate fractions. Next, we learned how to determine which solutions are extraneous solutions. We reviewed the fact that any value of a variable that makes the denominator of a rational expression zero must be excluded from the domain. In the same way, when a solution of a rational equation results in a zero in the denominator, that solution must be excluded. These solutions are called extraneous solutions.
Lesson 11-6 Adding and Subtracting Rational Expressions – We practiced adding and subtracting rational expressions with unlike denominators. We learned how to add rational expressions with unlike denominators by using the least common multiple of the denominators to get equivalent expressions with a common denominator.
Lesson 11-7 Mixed Expressions and Complex Fractions – We learned how to use complex fractions to solve problems. We simplified complex fractions involving monomials and polynomials.
Lesson 11-5 Dividing Polynomials – We practiced dividing rational expressions. We divided polynomials by monomials. Then we divided polynomials by binomials with long division. Hudson will remember to put parentheses around the term you are subtracting to distribute the negative one through the parentheses.
Lesson 11-4 Multiplying and Dividing Rational Expressions – We simplified expressions involving the quotient of monomials. Then we identified values excluded from the domain of a rational expression. Next, we simplified expressions and complex fractions.
Lesson 11-4 Multiplying and Dividing Rational Expression – Hudson and I worked on multiplying and dividing rational expressions. We went through examples showing how to multiply rational expressions of all monomials. We discovered how to factor a quadratic expression before simplifying a product of rational expressions involving polynomials that are not monomials.
Lesson 9-2 Solving Quadratic Equations and Lesson 9-4 Solving Quadratic Equations by Completing the Square – Hudson and I worked on factoring quadratic equations and finding the zero products. This is to prepare him for a test this week. Then we worked on learning the different conjugations of the verb ir-to go and the words describing pastimes or hobbies for a Spanish test tomorrow.
Lesson 9-4 Solving Quadratic Equations by Completing the Square – Hudson learned how to complete the square to write perfect square trinomials. He solved quadratic equations by completing the square. Then we worked on simplifying algebraic expressions by factoring out the greatest common factor. Some of the homework problems involved factoring out an algebraic expression.
