Learning Algebra Amber Elsner 8 th Grade Algebra Click for the next slide
Transcript
Slide 1
Slide 2
Learning Algebra Amber Elsner 8 th Grade Algebra Click for the
next slide
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Algebraic Expressions Distributive Properties Graphing
Combining Like Terms Multiplying Monomials Multiplying Binomials:
FOIL (smiling man) Solving Equations Multiplying Binomials: Box
Method Algebra Topics Review Question CLICK either the text or
image to learn each algebra topic!
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Algebraic Expressions Equation- a complete math sentence that
includes an equal sign Expression- a math sentence without an equal
sign Terms- separate values in an expression Variable- unknown
number, often represented by x Constant- a number that doesnt
change Coefficient- number that is multiplied by the variable
Equation- a complete math sentence that includes an equal sign
Expression- a math sentence without an equal sign Terms- separate
values in an expression Variable- unknown number, often represented
by x Constant- a number that doesnt change Coefficient- number that
is multiplied by the variable Click to go back to Algebra Topics =
2 Monomial- 1 term Ex: (xy) Binomial- 2 terms Ex: (xy zx)
Trinomial- 3 terms Ex: (xy zx + 4y) Quadnomial- 4 terms Ex: (xy zx
+ 4y 3) Monomial- 1 term Ex: (xy) Binomial- 2 terms Ex: (xy zx)
Trinomial- 3 terms Ex: (xy zx + 4y) Quadnomial- 4 terms Ex: (xy zx
+ 4y 3)
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Combining Like Terms Add or Subtract integers, combine
coefficients Keep operations with correct terms o 4x - 7x -3x Order
of the terms does not matter Example: 3y + 2x - 9y (combine 3y and
-9y) 2x - 6y (another way to write it) -6y + 2x Add or Subtract
integers, combine coefficients Keep operations with correct terms o
4x - 7x -3x Order of the terms does not matter Example: 3y + 2x -
9y (combine 3y and -9y) 2x - 6y (another way to write it) -6y + 2x
Click to go back to Algebra Topics
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Distributive Properties Click to go back to Algebra Topics
Note: These do not work with subtraction or division. Distribute
the x to the y and the z x (y + z) = xy + xz x (y z) = xy xz Note:
that the (+) and () signs separate the xy and the xz when the x is
distributed Distribute the x to the y and the z x (y + z) = xy + xz
x (y z) = xy xz Note: that the (+) and () signs separate the xy and
the xz when the x is distributed
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Multiplying Monomials Click to go back to Algebra Topics
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Multiplying Binomials: FOIL (smiling man) FOIL stands for: F:
multiply the first terms in each factor (x 2)(2x + 1) O: multiply
the outside terms in each factor (x 2)(2x + 1) I: multiply the
inside terms in each factor (x 2)(2x + 1) L: multiply the last
terms in each factor (x 2)(2x + 1) FOIL stands for: F: multiply the
first terms in each factor (x 2)(2x + 1) O: multiply the outside
terms in each factor (x 2)(2x + 1) I: multiply the inside terms in
each factor (x 2)(2x + 1) L: multiply the last terms in each factor
(x 2)(2x + 1) Click to go back to Algebra Topics Result from FOIL:
2x + x 4x 2 Simplify: 2x 3x 2 Result from FOIL: 2x + x 4x 2
Simplify: 2x 3x 2
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Multiplying Binomials: Box Method Create a two-by-two box One
factor goes on top The other goes on the side Signs should stay
with the correct number and variable Create a two-by-two box One
factor goes on top The other goes on the side Signs should stay
with the correct number and variable Click to go back to Algebra
Topics X X 2 + - 4 Multiply each factor in rows and in columns Top
left box: x Top right box: -2x Bottom left box: 4x Bottom right
box: -8 Multiply each factor in rows and in columns Top left box: x
Top right box: -2x Bottom left box: 4x Bottom right box: -8 Add
together each term x + 4x 2x 8 Combine like terms x + 2x 8 Add
together each term x + 4x 2x 8 Combine like terms x + 2x 8
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Graphing Use two axes Horizontal x-axis Vertical y-axis When x
and y axes meet they form 4 quadrants Labeled 1 to 4 in Roman
numerals Quadrant I is in top right Quadrant II is in top left
Quadrant III is in bottom left Quadrant IV is in bottom right If a
point is on the x or y axes, then that point is not located in any
quadrant. Use two axes Horizontal x-axis Vertical y-axis When x and
y axes meet they form 4 quadrants Labeled 1 to 4 in Roman numerals
Quadrant I is in top right Quadrant II is in top left Quadrant III
is in bottom left Quadrant IV is in bottom right If a point is on
the x or y axes, then that point is not located in any quadrant.
Click to go back to Algebra Topics Plotting points Written as (x,
y) Always start at the origin Center point of the graph (0, 0) Find
the position on the x-axis Locate the position on the y-axis Plot
where the two meet Plotting points Written as (x, y) Always start
at the origin Center point of the graph (0, 0) Find the position on
the x-axis Locate the position on the y-axis Plot where the two
meet
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Solving Equations Whatever you do to one side you MUST do to
the other side Why? To keep each side balanced! Whatever you do to
one side you MUST do to the other side Why? To keep each side
balanced! Click to go back to Algebra Topics Isolate variables by
using opposite operations Addition: use subtraction x + 1 = 5 - 1 -
1 x = 4 Subtraction: use addition x 2 = -6 + 2 + 2 x = -4 Isolate
variables by using opposite operations Addition: use subtraction x
+ 1 = 5 - 1 - 1 x = 4 Subtraction: use addition x 2 = -6 + 2 + 2 x
= -4 Multiplication: use division 3x = 21 3 3 x = 7 Division: use
multiplication x/3 = 5 * 3 x = 15 Multiplication: use division 3x =
21 3 3 x = 7 Division: use multiplication x/3 = 5 * 3 x = 15
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REVIEW QUESTION! What is the correct, simplified answer when
you multiply the binomial (2x 2)(x + 5) ? A. 2x 8x 102x 8x 10 B.2x
+ 8x 102x + 8x 10 C.2x + 12x + 102x + 12x + 10
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2x 8x 10 Click to go back to Review Question Watch the signs
when using the distributive property and multiplying the numbers.
Check your work and go back to try again
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Click to continue 2x + 8x 10 Correct! Great work! You
multiplied the binomial and simplified it correctly!
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Click to go back to Review Question Watch the signs when using
the distributive property and multiplying the numbers. 2x + 12x +
10 Check your work and go back to try again
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Congratulations! You have successfully completed learning some
basic algebra concepts! Click ALGEBRA to return to the title slide
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