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Algebra!!! Terms Terms can be all of the following • • • • Variables Whole numbers(constants) Integers(constants) Rationals ( fractions, decimals)(constants) • Variables and number together Example • X • (1,2,3,4,5,…. • (-3,-2,-1,0,1,2,3… • ½, 0.3 • 4x, 6x,1.2x Variable Definition • A symbol that represents a number . • Letters are popular • “x” is even more popular. • It is useful to use a letter of something that will remind you of what is missing. • N=number of people • T=time • D= distance Variable http://www.5min.com/Video/How-toUnderstand-Algebraic-Variables-181133000 Coefficient • Number( constant) in front of the variable • These are also terms • • • • 3x 7xy 8x 16s How is this useful? • If you want to try and find the perimeter of this square. s I would use “s” to represent my variable. My term would be s+s+s+s=4s 4s represents the perimeter of this square Expression Definition • A combination of terms • Number sentence Example • 2x +7 +(-3) Lets dissect this expression • • • • 6xy+ 7y+7-10 Variables: Terms: Coefficents: Evaluate expressions • Evaluate: giving something value or worth. • When we evaluate an expression we are giving it worth. • Example: • Your given the following expression • 3x+5-10 • Then you are told x=4 Evaluate expressions • Instead of writing x in the expression we change it for 4. • 3(4)+5-10=7 • Now the expression is worth 7. http://www.bbc.co.uk/education/mathsfile/sh ockwave/games/postie.html Home work • Pg 13 #1 (panorama) Like and unlike terms Like Terms • Terms are considered “like” if their variable are the same. • Therefore they have the same ending. 2x and 3x • “Apples with apples” • Like terms can be combined Unlike term • Terms are considered “unlike” if their variables are different. • 2x and 3xy • 6 and 7b • Unlike terms cannot be combined. Which Ones are like terms? • 3x • -5b • 6b 4b 10xy 8 7 6 -60xy 14x -23xy Simplifying Expressions • Making a complicated expression simple by combining like terms. • Example; • 3x+9+4x-7 * we are NOT solving! • 3x+9+4x-7 • 3x+4x=7x • 9-7=2 • 7x+2 Making an equation • Lets go back to the square example, • If I now know the perimeter of this square is 20 cm. • What is the length of the side? 1) First we put our term 4s that represents the perimeter. 2)4s equals 20 cm 20cm 4s=20 Translate the following in to equations Translate Translate Homework: • Worksheets Words to equations • The trick here is to define your variable first! • Therefore pick your letters to represent something in the problem. • Example: • A sum of a number and 10 gives you 15 Answer X+10=15 Example • The quotient of a number and 4 is 16. Answer Example • 3 years from now triple Eric's age will be 45. Answer • 3(x+3)=45 Homework • Math 300 4 Steps to Solving an Algebra Word Problem • • • • 1) Choose unknowns 2) Write equation 3) Solve equation 4) Write Answers Example • A rectangle has a perimeter of 100cm. Its length measures 10cm more than its width. We want to find the area of the rectangle. • 1) Unknowns: • Length =L • Width=L+10 • 2) Equation: • 2(L)+2(L+10)=100 Example • • • • • • • • 3) 2L+2L+20=100 4L+20=100 4L=100-20 4L=80 L=20cm W=L+10 W=20+10 4) Length is 20cm and the with is 30cm Perimeter Problems 1) Add all the sides together. (3x)+(3x)+(2x+1) 3x 3x 2) Collect like terms 8X+1 2x+1 Answer: 8x+1 Area Problems 2x 4x-2