Week one introduction to determining points for fantasy football.

1. Introduction to Orders of Operations and
Linear Equations

2. Order Of Operations
Rule 1: First perform any calculations inside
parentheses.
Rule 2: Next perform all multiplications and
divisions, working from left to right.
Rule 3: Lastly, perform all additions and
subtractions, working from left to right.

3. Example 3: Evaluate 9 - 5 ÷
(8 - 3) x 2 + 6
using the order
of operations.
Solution:
Step 1: 9 - 5 ÷ (8 - 3) x 2 = 9-5÷5x2+6 Parentheses
+6
Step 2: 9-5÷5x2+6 = 9-1x2+6 Division
Step 3: 9-1x2+6 = 9-2+6 Multiplication
Step 4: 9-2+6 = 7+6 Subtraction
Step 5: 7+6 = 13 Addition
In Examples 2 and 3, you will notice that multiplication and division were evaluated
from left to right according to Rule 2. Similarly, addition and subtraction were evaluated
from left to right, according to Rule 3.

4. Example 2: Evaluate 3 + 6 x
(5 + 4) ÷ 3 - 7
using the order
of operations.
Solution:
Step 1: 3 + 6 x (5 + 4) ÷ 3 = 3 + 6 x 9 ÷ 3 - 7 Parentheses
-7
Step 2: 3+6x9÷3-7 = 3 + 54 ÷ 3 - 7 Multiplication
Step 3: 3 + 54 ÷ 3 - 7 = 3 + 18 - 7 Division
Step 4: 3 + 18 - 7 = 21 - 7 Addition
Step 5: 21 - 7 = 14 Subtraction

5. Example Evaluate
4: 150 ÷ (6
+ 3 x 8) -
5 using
the
order of
operatio
ns.
Solution
:
Step 1: 150 ÷ (6 = 150 ÷ (6 + 24) - 5 Multiplication inside
+ 3 x 8) Parentheses
-5
Step 2: 150 ÷ (6 = 150 ÷ 30 - 5 Addition inside Parentheses
+ 24) - 5
Step 3: 150 ÷ = 5-5 Division
30 - 5
Step 4: 5 - 5 = 0 Subtracti
When two or more operations occur inside a set of parentheses, these operations should
be evaluated according to Rules 2 and 3. This is done in Example 4 below.

6. Example 5: Evaluate the arithmetic expression below:
Solution:
This problem includes a fraction bar (also called a
vinculum), which means we must divide the
numerator by the denominator. However, we must
first perform all calculations above and below the
fraction bar BEFORE dividing.
Thus
Evaluating this expression, we get:

8. Multiplying a Fraction and a Whole Number
4 X 2/3 =
4/1 X 2/3 = 2/3 + 2/3 +2/3+ 2/3 = 8/3

9. Multiplying a Fraction and a Whole Number
4 X 2/3 =
4/1 X 2/3 = 2/3 + 2/3 +2/3+ 2/3 = 8/3

10. Multiplying a Fraction and a Whole Number
4 X 2/3 =
4/1 X 2/3 = 2/3 + 2/3 +2/3+ 2/3 = 8/3

11. Multiplying a Fraction and a Whole Number
4 X 2/3 =
4/1 X 2/3 = 2/3 + 2/3 +2/3+ 2/3 = 8/3

12. Multiplying a Fraction and a Whole Number
4 X 2/3 =
4/1 X 2/3 = 2/3 + 2/3 +2/3+ 2/3 = 8/3

13. Problem One
T= 2
V= 1
P=14
R=3
C=0
I=2
F=0

14. Problem Two
T= 3
V= 0
P=1
R=17
C=7
I=4
F=1