- The document discusses an upcoming math final exam and provides examples to review rational equations, expressions with fractions, and formulas. - Topics to review for the final exam include translations, order of operations, integers, and simplifying expressions. Example problems are provided to work through. - Additional examples cover solving equations with variables on both sides, working with fractional equations, and operations with fractions and decimals such as adding, subtracting, multiplying, and dividing.

1. Today…
 Khan Academy Schedule
 Review for Final Exam This Week
 Notebooks Prepared; leave Friday
 Class Work

2.  Solving Rational Equations 1
You have until Tuesday evening to complete this topic. Ask
today if you have questions.
 Due to Final Exams, No Khan Academy for November, 9th
November 16, 2014—7:00 pm
 Inequalities on a Number Line
 One-Step Inequalities
 Constructing Linear Equation Word Problems

4. Topic Review: Rational Equations 1
Next Week: Wednesday, Final Exam Part I
A) Translations
B) Order of Operations
C) Integers
D) Simplifying Expressions

5. 1. Find two consecutive numbers where the smaller
number plus four times the larger number equals 39
How do we write two consecutive numbers?
x + x + 1
4( ) = 39
Four times the larger number?
2. The product of two numbers is 30. One of the numbers
is x. What is the other number? xy = 30, y must be.... ퟑퟎ
x y
(6)(5) = 30 풙
6 •
ퟑퟎ
ퟔ
3. Ten times the difference of twice a number and six is
52. What is the number?

7. 13 - 5•-3 + (7 -3•8) -18/3 ((13--15)+(7-3×8))-18/3
(28+(7-3×8))-18/3
(28+(7-24))-18/3
(28+-17)-18/3
11-18/3
11-6
5

8. Unlike equations, when simplifying expressions with
fractions, you cannot clear fractions by multiplying by a
common denominator. Why? What is different about
simplifying and solving?
What is the simplified form?
Remember, 6xy and 12yx are like terms and can be combined.
-
ퟏ
ퟑ
x +
ퟏ
ퟔ
x =
− ퟔ+ퟑ
ퟏퟖ
x =
ퟑ
ퟏퟖ
x =
ퟏ
ퟔ
x
-4(-2b – 5) – 3(2b + 4c) + (-1 – 10b) - 7

9. Thursday, Final Exam Part II
I. Equations: All types
II. Formulas
III. Fractions/Decimals

10. Solving Equations with Variables on Both Sides
-8x - 2 = -4x + 7
This problem can be solved by starting with any of the four
terms first. Solve the problem 4 different ways, each time
starting with the next term.
1. -8x - 2 = -4x + 7; begin with -8x - 2 = 4x + 7; solve
2. -8x - 2 = -4x + 7; begin with....... - 8x = -4x + 9; solve
3. -8x - 2 = -4x + 7; begin with....... - 4x – 2 = + 7; solve
4. -8x - 2 = -4x + 7; begin with.... - 8x – 9 = - 4x, solve
As you can see, there isn’t one correct way to solve an equation.
Some methods are simply easier than others.

11. If -1 = 4 – 5, then 1 =...
Equations:
We multiplied by -1. Algebra is
understanding and applying the
patterns (rules) of numbers. It isn’t
creating rules for numbers; it is the
truth of numbers.
How do we make this fraction positive?
−ퟒ
ퟏ
After multiplying by -1, Why isn’t the fraction
- 1 = 4
ퟒ
?
−ퟏ
A) N =
푺−푨
푺푫
B) N =
푺푫
푺+ 푫
C)N =
푺+푨
푺푫
D)N =
푨−푺
푺푫
E) N =
푺+푫
푺푨
Fractions are a single number,
not two separate numbers
−ퟒ
ퟏ
This single number is negative.
When multiplied by -1, it
becomes positive.

12. Fractional Equations:
There are several ways fractions can appear in equations, but
the goal is always to clear the fractions the easiest way possible.
C.
ퟏ
ퟑ
x – 3 = 9
1. Combine like terms if easier. Are there
like terms?
Yes, there are, but not real easy to combine
them. Skip for now.
2. Instead, let's clear the fractions by multiplying each term
by the number which cancels the denominator
ퟑ
ퟏ
(
ퟏ
ퟑ
x) -
ퟑ
ퟏ
(
ퟏ
ퟑ
) =
ퟑ
ퟏ
(
ퟗ
ퟏ
);
3. Isolate the variable on the left using the inverse
property, and divide by the any coefficient.
x = 28
x - 1 = 27

13. C.
ퟏ
ퟐ
x - 3 =
Fractional Equations:
ퟏ
ퟓ
x + 3
1.. Combine like terms?
2. Here we have 2 different denominators, so we find the
Least Common Denominator (LCD); The LCD of 2 and 5 is 10.
Now we have:
Yes
ퟏ
ퟐ
x =
ퟏ
ퟓ
x + 6
5x = 2x + 60;
Completing the steps we get: 5x - 2x = 3x = 60; x = 20
Other Equations:
1. 9p = 3k(p + 5) for k
n = (2,0)

14. Formulas
1. The width of a rectangle is 2 more than one-half the length.
The perimeter is 89 yards. Find the length & width.
P = 89
2. The A's played 72 games. They won 15 more games
than they lost. How many games did they win and lose?
3. A triangular piece of land has an area of 120 ft. The
longest side is 30 ft. long and the shortest side is 10 feet
long. What is the length of the third side?
x
(h)
30
A =120
10
What do we know?
Formula for area of
triangle?
A =
풃풉
ퟐ
Not necessary for
our solution
W = .5L + 2
P = 2L + 2W
Solve for h (x)
ퟐ푨
ퟏퟎ
= h

15. Fractions & Decimals:
Adding & Subtracting: Cross-Multiply
Before solving, estimate solution as positive or negative number.
ퟑ
ퟒ
-
ퟑ
ퟓ
ퟐ
ퟑ
2
ퟏ
ퟒ
- (-4
)
Multiplying & Dividing Fractions:
ퟏ
ퟒ
•
ퟏ
ퟒ
ퟏ
ퟒ
÷
ퟏ
ퟒ