This document contains notes from a math class that covered several topics: - Warm-up with Khan Academy on fractions and percents - Reviewing fraction and percent conversions - Solving absolute value equations - The notes provide examples and steps for solving absolute value equations, changing fractions to decimals, and ordering fractions using cross-multiplication. Examples are worked through to demonstrate the process.

1. Today:
Warm-Up: Khan Academy Topics
 Review Fraction/Percent Conversions
 Absolute Value Equations
Class Work
October 20, 2014

7. A riparian buffer is an area around a stream that’s covered in
vegetation. It protects the water in the stream from activity
happening near its location.
A farm is located near a riparian
buffer. The buffer begins S feet
from the edge of the farm and
ends B feet from the farm. How
wide is the riparian buffer?

8. 8 12
S B
B S
12 8

9. =
ퟓ
ퟒ
+ .2 =
ퟓ
ퟒ
+
ퟏ
ퟓ
=
ퟐퟗ
ퟐퟎ
= 1.45 kilometers

10. Create a visual of some type
Cross Multiply? Y or N
ퟏퟕퟏ
ퟐퟎ
= 8
ퟏퟏ
ퟐퟎ
= 8.8 meters

12. How to easily order fractions using cross-multiplication
42 45
5/6 is > 7/9
Order from least to greatest:
Instead of finding a
common denominator
for 6 and 9,
In this case, however...
Be aware and flexible, take
the path of least resistance.

13. State whether the first fraction is <, >, or = to the second.
Changing Fractions to Decimals
There are three methods to changing fractions to decimals. The
method used is determined by the denominator of the fraction.
1. If the denominator is a place value: 10, 100, 1000, etc. The
decimal will match the place value of the denominator.

14. Changing Fractions to Decimals
2. If the denominator is a factor of a place value (can be divided
evenly by 10, 100, 1000, etc.), multiply by the number needed
for the product to equal the closest place value.
3. If the denominator is not a factor of a place value, then the
numerator is divided by the denominator.

15. Solving Absolute Value Equations
Solve x = 7
Because the |x|could be positive or negative, we must
solve for both possibilities.
When solving an equation, isolate the absolute value
expression first.
Rewrite the equation as two separate equations.
Once the absolute value is isolated, the grouping symbols
can be taken off.
The solutions are:
x = 7 x = -7

16. Solving Absolute Value Equations
To solve (after the absolute value is
isolated), split into two equations:
• One with a positive 6
• The other with the opposite of six, -6
• Then solve each individually
|ퟑ풙| = ퟔ
ퟑ풙 = ퟔ ퟑ풙 = −ퟔ
What are the solutions to the equation 3푥 = 6
x = 2; x = -2

17. What is the solution for this equation?
Rewrite the absolute value equation as two equations.
2x – 3 = 9 or 2x – 3 = –9 Rewrite as two equations.
Solve each equation separately.
x = –6 or x = 3
x = –3 or x = 6
x = –6 or x = 4
x = –3 or x = 4
2x – 3 = 9
Always check your solutions.

18. Solving Absolute Value Equations
Solve 3 2 x + 7 – 5 = 4
First, rewrite the equation in the form a x + b = c
3 2x + 7 – 5 = 4 Write original equation.
3 2x + 7 = 9 Add 5 to each side.
2x + 7 = 3 Divide each side by 3.
Next, rewrite as two equations, then solve each one.
2x + 7 = 3 or 2x + 7 = –3
X = -2, or x = -5

19. Decide if an equation has any solutions
Solve 3x + 5 + 6 = 2
3x + 5 + 6 = 2 Write original equation.
3x + 5 = –4 Subtract 6 from each side.
What’s the next step?
The absolute value of a number is never
negative. So, there are no solutions.
Decide if an equation has any solutions
4 t + 9 – 5 = - 3
Are there any solutions?
That decision cannot be made until the
absolute value is isolated.

22. An absolute value equation can have two, one,
or even no solutions.

23. Solve the equation.
2 m – 5 + 4 = 2
–3 n + 2 – 7 = –10
ANSWER no solution
ANSWER –1, –3
An NFL football must be inflated to an air pressure of 13 psi
with an absolute error of 0.5 psi. Find the minimum and
maximum acceptable air pressures for an NFL football.
ANSWER 12.5 psi, 13.5 psi

24. 5. ANSWER 16, –2
ANSWER 7.4, –7.4
Solve the equation.
r – 7 = 9
6. 2 s + 4.1 = 18.9
ANSWER –3, –15