Exponents and Order of Operations

download report

Transcript Exponents and Order of Operations

IS means = sign
Writing Equations:
“2 more than twice a number is 5”
2 +
2x
= 5
2 + 2x = 5
It can be any letter. We usually
see x and y used as variables.
“a number divided by 3 is 8”
x
or

x 8
3
Sometimes you have to decide
what the variable is…
3 = 8
“the sum of a number and ten is the same as 15”
x + 10 = 15
“The total pay is the number of hours
times 6.50”
{Sometimes, two variables are needed}
Writing an Equation…
Define variables and identify key parts of the problem…
Track One Media sells all CDs for $12 each. Write an
equation for the total cost of a given number of CDs.
Number of
CDs
Cost
1
$8.50
2
$17.00
3
$25.50
4
$34.00
This table shows the relationship between
number of CDs and cost.
How much is 1 CD?
T = $8.50n
Number of
CDs
Cost
1
$8.50
C = total cost for CDs
2
$17.00
n = number of CDs bought
3
$25.50
4
$34.00
Cost = $8.50 times (number of CDs)
C = 8.50 n
We use a table of values to represent a
relationship.
Number of
hours
Total pay in
dollars
5
40
10
80
15
120
20
160
From the table, we can come up with an
equation.
Total pay = (number of hours) times (hourly pay)
What is the hourly pay?
$8 per hour
Total pay = 8 (number of hours)
T = 8h
Write an equation for the data below…
# of
Hours
8
Total Pay
12
$60
16
$80
$40
Exponents and Order of
Operations
Math 1 Sept 9
Check your skills
Find each Product
•
•
•
•
4 x4
7x7
5x5
9x9
Perform the indicated operations
•
•
•
•
3 + 12 – 8
4–2+9
5x5+7
30 ÷ 6 x 2
To simplify an expression, we write it in the simplest
form.
Example: Instead of 2 + 3 + 5, we write 10.
Instead of 2 · 8 + 2 · 3, we write 22.
We use order of operations to help us get the
right answer. PEMDAS
Parentheses first, then exponents, then
multiplication and division, then addition and
subtraction.
In the above example, we multiply first and then
add.
An exponent tells you how many times to multiply a
number (the base) by itself.
24
Means 2 times 2 times 2 times 2
This is also read as
Or 2 · 2 · 2 · 2
“2 to the 4th power”
A power has two
parts, a base and
an exponent, such
as 4
2
2
4
is 16 in simplest form.
Order of Operations
• Perform any operations inside grouping symbols first. i.e brackets,
parenthesis, curly lines.
• Simplify powers
• Multiply and Divide left to right
• Add and Subtract left to right
Always follow order of operations starting with the
inside parentheses.
PLEASE EXCUSE MY DEAR AUNT SALLY
P
Parentheses
E
Exponents
M Multiplication
D
Division
A
Addition
S
Subtraction
}
}
Left to right when
multiplication and
division are the only
operations left in the
problem
Left to right when
addition and
subtraction are the
only operations left
in the problem
Simplifying a Numerical Expression
• Numerical Expression = a expression with numbers only
Simplify: 25 – 8 × 2 + 32
25 – 8 × 2 + (3× 3)
25 – 8 × 2 + 9
25 – 16 + 9
18
• 6 – 10 ÷ 5
• 3 * 6 – 42 ÷ 2
• 4 * 7 + 4 ÷ 22
• 53 + 90 ÷ 10
Remember order of operation
•4
• 10
• 29
• 134
We evaluate expressions by plugging
numbers in for the variables.
Example:
Evaluate the expression for c = 5
and d = 2.
2c + 3d
2(5) + 3(2)
10 + 6
16
Simplifying an Expression With
Parentheses
• When you simplify expressions with parentheses, work within the
parentheses FIRST.
• Lets Try! Simplify:
• 15(13 - 7) ÷ (8 – 5)
15(13-7) ÷ (8 -5) = 15(6) ÷ 3
= 90 ÷ 3
= 30
Evaluate for x = 11 and y = 8
xy 2
(11)(8)2
(11)(8×8)
(11)(64) = 704
Now you Try:
•
•
(5 + 3) ÷ 2 + (52 – 3)
8 ÷ (9 – 7) + (13 ÷ 2)
Evaluating Expressions with Exponents
• The base for an exponent is the number, variable, or expression
directly to the left of the exponent.
• For example:
• B2  the base would be “B” for exponent
• 63  the base for “3” would be “6”
“2”
Evaluate the expression if m = 3, p = 7, and q = 4
mp  q
2
 3 7    4 
 3 49    4 
2
147  4
143
Evaluate the expression if m = 3, p = 7, and q = 4

m p2  q
3  72  4 
3  49  4 
3  45 
135
