2 Rational ExpressionsRational Expressions are fractions (ratios) that contain polynomial expressions in the numerator and denominator.Examples:
3 Rational Expressions Simplifying Rational Expressions with Monomial Numerators and DenominatorsMethod 1: Use laws of exponentsMethod 2: Expand and divide out common factors
4 Rational Expressions A) B) Simplifying Rational Expressions with Polynomial Numerators and DenominatorsFactor the numerator and denominatorDivide out common factorsRemember: Monomials can only be simplified with monomials and binomials can only be simplified with binomials that are exactly the same.A)B)
5 Rational ExpressionsWhen multiplying rational expressions, factor all the numerators and denominators. Divide out common factors.Factor all the numerators and denominators!
6 Rational Expressions When dividing rational expressions… Keep, Change, FlipFactor all the numerators and denominatorsDivide out common factorsKeep the first fractionChange division to multiplicationFlip the second fraction (reciprocal)
7 Rational ExpressionsWhen adding and subtracting rational expressions, find a common denominator if necessary.Create equivalent fractions using the common denominator(Multiply by FOOs).Add or subtract numerators and keep the denominator the same.Simplify your final answer if possible.FORM OF ONEEx:
8 Rational ExpressionsWhat is the sum of and expressed in simplest form?Add numerators andkeep the denominator.Simplify by factoring the numerator and denominator.
9 Rational Expressions LCD (Least Common Denominator): 9x2 FOO FOO Find equivalent fractions with a common denominator by multiply by a FOO (form of one).
10 Rational Expressions 8x(x + 12) = 2x(2x + 4) 8x2 + 96x = 4x2 + 8x When solving rational equations (equations with algebraic fractions), combine fractions and set up a proportion. Remember: A common denominator is needed to add or subtract fractions.8x(x + 12) = 2x(2x + 4)8x2 + 96x = 4x2 + 8x4x2 + 88x = 04x(x + 11) = 04x = x + 11 = 0x = x = -11FOOFOOReject 0 because it makes the equation undefined.Solution: x = -11
11 Scientific Notation Representing Numbers in Scientific Notation If this a skill you have not mastered and need additional instruction,re-watchFLIP #3.
12 Scientific Notation Multiplying Numbers in Scientific Notation Use the commutative property and laws of exponentsCalculator Corner:Press MODESelect SCI (see top row) , ENTERPress 2nd MODE to return to home screenEnter expression into the calculator (use the expression on this slide to practice)(4x10^5)(3.2x10^-9)5) Press ENTER6) The expression 1.28E-3 means 1.28 x 10-3Go to MODE and select NORMAL to exit scientific notation
13 Scientific Notation Dividing Numbers in Scientific Notation Calculator Corner:Press MODESelect SCI (see top row) , ENTERPress 2nd MODE to return to home screenEnter expression into the calculator (use the expression on this slide to practice)Put the numerator and denominator in ( )(5.6x10^-12)/(4x10^6)6) Press ENTER7) The expression 1.4E-18 means 1.4 x 10-18Go to MODE and select NORMAL to exit scientificnotation
14 Trigonometry Trigonometric Ratios What ratio represents the sine of the indicated angle pictured to the right?Answer: (1)
15 Trigonometry Finding Sides of a Right Triangle Use the Pythagorean Theorem when given two sidesUse Trigonometry when given a side and an anglePythagorean Theorem SOH CAH TOASubstitute known values into the trig ratio. Solve for the variable by cross multiplying.a2 + b2 = c2= c2= c225 = c25 = cCalculator must be in degrees(See MODE)
16 Trigonometry Finding Angles of a Right Triangle > Use inverse trig ratiosFind the measure of the indicated angle to the nearest degree.Calculator:2nd TAN
17 TrigonometryA 50 ft. ladder leans against a building. The foot of the ladder is 35 feet from the building. To the nearest degree, find the measure of the angle that the ladder makes with the ground.Are you looking for an angle or side?Trig Ratio or Inverse Trig Ratio?Draw a picture of the situationLooking for this angleRemember: Calculator must be in degrees in order to do a trigonometry problem. Go to Mode and highlight degree (ENTER)
18 Now it’s your turn to review on your own Now it’s your turn to review on your own! Use the information presented today to help you practice questions from the Regents Exams in the Green Book. See halgebra.org for the answer keys. Integrated Algebra Regents Review #2 Monday, June 16th BE THERE!