7th Grade Algebra A RSM

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7th Grade Algebra (A?????? ???????? ??????) RSM

• First Trimester
• (?????? ???????)
• By Minas Zahopoulos

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Table of Contents
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• Rate, Time, Distance..Slides 2-4
• ????????, B????, ? P???????????
  ???? 2-4
• Equations with Fractions...Slides
  5 6
• Y???????? ? ???????? ........?
  ????? 5 6
• Mixture ProblemsSlides 8 9
• ???????? ?????.......??????
  8 9
• Powers....Slide 10
• ??????? ..............???
  ?? 10
• Exponents Polynomial.Slides
  11-15
• ??????? ???????????..??????
  11-15
• Credits.Slide 16
• ??????.......?????? 16

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Rate, Time and Distance
The Formulas R D T T D R D R
T Average Speed Ave Speed
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How To Put it Into Use (simple)
Key Joe Jan Start
Question Joe and Jan leave their house to go to
their friends house in opposite directions. Joes
runs one mile per second and Jan runs 2 mps. How
far apart are they in an hour?
Solution
1 mps 2 mps
miles 3600 seconds miles 2
-------- x -------------- 7200 -------
second 1 hour hour
Hint Remember to look at the units and change
them so they are all the same!
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How To Put it Into Use (advanced)
Question Pippin and Sam are painting a fence.
Sam could paint the whole fence alone in 12
hours. Pippin could paint the whole fence alone
in 8 hours. Sam starts painting at 1 p.m. and
Pippin joins him at 3 p.m. At what time do they
finish?
Solution
Rate Time Distance
5 ---- 24
5 --- 6
x

x

4 hours
Answer They will finish at 7 p.m. (3 p.m. 4
hours 7 p.m.)
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Solving Equations with Fractions

• Solving equations with fractions is quite easy.
  All you need to do is remember your Least Common
  Multiples and how to solve a simple equation.
• e.g. If you know how to calculate and solve
  these
• OR

THEN
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Combining the Two!
When you cross out the 4 (because 4 is divisible
by 12) it becomes a 1 and the 12 becomes a 3.
Least Common Multiple of 4 and 3
Etc
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Mixture Problems!
Mixture Problems are easier when you draw a
diagram. The diagram must have three or more
boxes/beakers, an equal sign, and arithmetic
operations. Like this
Percent or variable
Percent or variable
Percent or variable


Number, Number /- a variable, or a variable
Number, Number /- a variable, or a variable
Number, Number /- a variable, or a variable
Inside the box is the percent of concentration
and under it is how much of it there is in the
box.
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Lets TRY it out!
Chris has 3 gallons of a solution that is 30
percent antifreeze, which he wants to use to
winterize his car. How much pure antifreeze
should he add to this solution so that the new
solution will be 65 percent antifreeze?
65


100
30
3
3 x
x
Change into decimal (.3) then multiply by 3.
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Powers
Remember These 9 GOLDEN Rules
(REMEMBER a?0, b?0 and y, x, and n are real
numbers!)
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Polynomials
Poly comes from the Greek word many.
Polynomials have more than one term. Monomials
are also polynomials. The sign before the term
says whether it is positive or negative. LIKE
TERMS terms that have the same coefficient and
exponents and can be added and subtracted. e.g.
10xy²z³ - 3xy²z³ 7xy²z³ UNLIKE TERMS terms
that DO NOT have the same coefficient and
exponents and CANNOT be added or subtracted e.g.
xyz² - xyz
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What is a monomial?

• Mono comes from the Greek word only or one.
  That is exactly what it means in mathematics, ONE
  TERM. A monomial does NOT contain a -/ sign.
• e.g. 12, 34², -3, ³, 5y²
• 4 ²

Exponent
Base
Coefficient
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What is a binomial?

• Bi comes from the Latin word two. That is
  exactly what it means in mathematics, TWO TERMS.
  A binomial contains a -/ sign and two terms.
• e.g. 12 34², -3y³ - ³, 5y² - 2cz²s³c
• 4 ² - 12

Constant
Leading Term
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What is a trinomial?

• Tri comes from the Latin word three. That is
  exactly what it means in mathematics, THREE
  TERMS. A trinomial contains a -/ sign and three
  terms.
• e.g. 12 34² - xc³, -3y³ - ³ 6, 5y² -
  2cz²s³c cx²
• 4 ² 7 ³ - 12

Constant
Leading Term
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• Not everything is a polynomial!
• 6x-2 is NOT a polynomial because the variable
  has a negative exponent.
• is NOT a polynomial because the variable is in
  the denominator.
• vx is NOT a polynomial either because the
  variable is inside a radical.

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Thank You for Watching! ??????? ?? ??????????

• References
• http//www.google.com/search?hlenqmixtureprob
  lemsbtnGGoogleSearchaq0oqmixture
• http//www.themathpage.com/alg/equations-fraction
  s.htm
• http//www.artofproblemsolving.com/Books/IntroAlg
  ebra/exc2.pdf