Transcript Exponents and order of operations

Exponents
and
Order of Operations
Exponents
• Exponent: how many
times to multiply the
base by itself
14⁴
14 is the base
4 is the exponent
(14)(14)(14)(14) = 14⁴
2⁵ = (2)(2)(2)(2)(2) = 32
(⅜)² = (⅜)(⅜) = 9/64
4⁴ = _________
5² = ______
(¾)² = ________
(10)³ = __________
(4)(4)(4)(4) = 256
(5)(5) = 25
(¾) (¾) = 9/16
(10)(10)(10) = 1000
Solve the following problem below:
16 – 7 + 108 ÷ 6(3)²
Think about things in your life that you must use
a particular order.
Order of Operations
• To solve problems with
numerous operations
we must use an order.
–
–
–
–
–
–
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication/Division
and
Addition/Subtraction
have an exception!
- You must perform the
operations from left to
right
Example:
(5+3) ÷ 2 + (5² - 3)
(5+3) ÷ 2 + (25 -3)
8 ÷ 2 + 22
4 + 22
26
Example:
18 – 7 + 9 – 10 + 4
11 + 9 – 10 + 4
20 – 10 + 4
10 + 4
14
8² - 4
72
64 – 4
72
60
72
5
6
12 + 3[18-5(16-13)]
12 + 3[18-5(3)]
12 + 3[18 – 15]
12 + 3[3]
12 + 9
21
3 + | 7-4 | + 3²
8-5
8 ÷ (9-7) + (14 ÷2)²
8 ÷ 2 + 7²
8 ÷ 2 + 49
4 + 49
53
3 + | 3 | + 3²
8-5
3 + 3 + 3²
8–5
3+3+9
8-5
15
3
5
Evaluating Expressions and Equations
Algebraic Expression
a collection of numbers,
variables, operation
symbols, and grouping
symbols
Example:
4
6x⁹(8yt)
5x + 9
Expressions do not have
equal signs
Equation
a mathematical
statement that two
expressions have equal
value
Example:
5 + p = 10
21 – 4 = 17
I = PRT
Equations have equal signs
Evaluating Algebraic Expressions
• Substitute the given
values for the variables
assigned to it
Example:
x = 4, y = 9, z = 10
5x + y - z
5(4) + 9 – 10
20 + 9 – 10 =
29 – 10 = 19
Evaluate the expression
when x = 1 and y = 4
1). 2y – x
2). X + 5
Y Y
3). y² - x²
1). 7
2). 3/2
3). 15
Solution of an Equation
• Substitute the given value
for the variable
• Check to see if both
expressions are equal
• If they are then the given
value is a solution
Determine if the given
number is a solution
when x = 3
Example:
Is x = 4 a solution for
12x – 6 = 18
12(4) – 6 = 18
48 – 6 = 18
42 – 18 No x =4 is not a solution
(3)² - 8 = 4 -3
9 – 8 = 4 -3
1=1
yes
1). X² - 8 = 4 – x
Group Work
• In your small groups, think of how many
words mean these mathematical terms
– Addition
– Subtraction
– Multiplication
– Division
– Equality
Translating Expressions and Equations
• On p. 28 there are a list of
words
• Example:
The product of a number a
five
(x)5 = 5x
Always let a variable
represent an unknown
number.
1.
2.
3.
a number added to seven
Twice a number, plus one
Twice a number, decreased
by 1 is 99.
Answers:
1). B + 7
2). 2h + 1
3). 2x – 1 = 00
Pay Close Attention
How do you translate 5
subtracted from 6 ?
How do you translate “ten
less than a number”?
6 -5
X – 10
Whenever you see
“subtracted from”, the
second number comes
first.
“Number less 10”
X – 10