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Chapter 11 Rational Equations and Functions Monday March 19 11.1 26 11.5 April 2 Tuesday 20 11.2 27 11.6 3 Wednesday 21 11.3 28 11.6 4 9 10 11.7 17 Ch 11 Test 11 11.8 16 review Thursday 22 11.3 29 Quiz 11.1-11.6 5 Holy Thursday 12 11.8 Friday 23 11.4 30 11.7 6 Good Friday 13 review Below is an estimate of when assignments will be due. Dates may be adjusted. Date Assigned Assignment -due next day Monday, March 19 11.1 p646 18,22,26,30,34,38,44,47,48 Tuesday, March 20 11.2 p653 #14-32 even, 33-41,45 Wednesday, March 21 11.3 p659 #12-36 even, 37,38 Thursday, March 22 11.3 p660 #42,47-49; p662 1-9 odd Friday, March 23 Monday, March 26 Tuesday, March 27 Wednesday, March 28 Thursday, March 29 11.4 p667 10-30 even, 31, 40,41,50 11.5 p673 12-34 even, 52,59 11.6 p679 10-32 even, 36-38, 42-48 even Study for quiz on 11.1-11.6 11.7 p687 16-22 even; 23-26 all; 28-48 even Tuesday, April 10 Wednesday, April 11 Thursday, April 12 Friday, April 13 quiz 1 p662; quiz 2 p682 11.8 p694 14,16,18,22,24,26,30, 32,34,36 p700-702 #2-28 even Study for Ch 11 Test 11.1 Ratio and proportion Proportion Extremes Reciprocal Property: if two ratios are equal, then their reciprocals are equal; a/b=c/d then b/a=d/c Cross product property: product of extremes=product of means if a/b=c/d, then ad=bc USE ONLY IN PROPORTIONS Extraneous solution 11.2 Percent 11.3 Direct and inverse variation Direct variation: y=kx Indirect variation: y=k/x Graph and compare: y=2x and y=2/x 11.4 Simplifying rational expressions Rational number: # that can be written as the quotient of two integers, eg. 1/2, 4/3, 7/1 Rational expression: a fraction whose numerator, denominator, or both are nonzero polynomials -is undefined when the denominator is equal to zero Simplified: in a fraction, the numerator and denominator do not have any common factors other than + or - 1 - ac/bc is simplified to a/b Are the original expression and the simplified expression defined for the same values of the variable? A rational expression is undefined when the denominator=0 Natural or counting numbers: 1,2,3,4,5.. Whole numbers: 0,1,2,3,4,5... Integers: …-3,-2,-1,0,1,2,3... Rational numbers: can be written as an integer/a natural #, or a/b b not equal zero, can also be written as either a terminating decimal or a repeating decimal; eg 19/8=2.374; 1/3 =.3333... Irrational number: a number whose decimal form is nonterminating and nonrepeating eg √5 or pi√3 pi/2 11.5 Multiplying and dividing rational expressions To multiply: multiply numerators and denominators, then factor and divide out common factors. To divide: multiply by the reciprocal of the divisor, then factor and divide out common factors. 11.6 Adding and subtracting rational expressions With Like Denominators: eg. 1/4+2/4=3/4; 5/6-2/6=3/6 To add, add the numerators: a/c +b/c = (a+b)/c To subtract, subtract the numerator: a/c-b/c=(a-b)/c With Unlike Denominators: eg. 1/4+2/6= 3/12+4/12=7/12 find the least common denominator, then add or subtract 11.7 Dividing polynomials 11.8 Rational equations and functions