Transcript Algebra!!! - msmandigo

Algebra!!!
Terms
Terms can be all of the following
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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
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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
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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
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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
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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
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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