Download Exponents-and-Order-of-Operations-PPT

Exponents
&
Order of
Operations
Repeated Addition problems
transform into multiplication problems
Example:
3+3+3+3+3= 15
But that takes so long to write out doesn’t it?
It is for this reason, multiplication was introduced.

So the same addition problems becomes 3 x5= 15
We use multiplication for repeated addition problems because it makes them
easier to write and solve.
Repeated multiplication becomes…
2x2x2x2x2=
This problem can be simplified using a short
hand way to write a repeated
multiplication problem called EXPONENTS.
2x2x2x2x2=
What are the parts of an expression
with an exponent?
Power
5
2
Exponent
Base
So this expression means 2 raised to the 5th power
How do we solve an expression with
an exponent?
5
2
First we need to remember that the exponent tells us how many times
to multiply the base number as a factor.
So 25 really means 2 x 2 x 2 x 2 x 2
How do we solve an expression with
an exponent?
5
2
A common misconception is to think that we solve exponents the
same way we do regular multiplication problems.
25 does not mean 2x5
How do we solve an expression with
an exponent?
5
2
(exponent in expanded form)
2x2x2x2x2
In order to solve, we will find the partial product
2x2x2x2x2
4 x 4 x2
16
x 2 = 32
How do we solve an expression with
an exponent?
2 = 32
5
Practice problems
Write the following with an exponent, THEN solve.
1. 5 × 5 × 5
2. 10 × 10
3. 0.2 × 0.2 × 0.2
4. 8 × 8 × 8 × 8 × 8
5. 3 × 3 × 3 × 3 × 3 × 3 × 3
6.
1/
4
× 1/4 × 1/4
7. 2 × 2 × 2 × 2 × 2 × 2 × 2
8. 6.5 × 6.5
Practice problems
Write each power as a product of the same factor. Then find the value.
1. 35
2. 122
3. 63
4. 48
5. (1/2) 3
6. 26
7. 5.43
8. 6.92
Order of
Operation
P.E.M.D.A.S
In your groups, solve this expression.
Be ready to post your answer and work on the board
and explain and defend the steps you used to solve
it.
3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2=
What does it mean?
Please Excuse My Dear Aunt Sally
Purple Elephants Might Destroy A
School
P.E.M.D.A.S. is a mnemonic device we
use to help us remember the order of
operations when solving expressions
Each letter stands for a type of operationBasically when you are solving an expression if it
isn’t a letter or number, it is an operation.
{} [] () 𝑟 2 x ÷ + P.E.M.D.A.S helps us to remember what order we
complete the operations in expression.
What does it REALLY mean?
P = Parenthesis
or any type of grouping symbols
()
{}
[]
What does it REALLY mean?
E= Exponents
6
2
2
10
4
8
What does it REALLY mean?
Multiply & Divide
4x5 or 10 ÷ 2
Always complete left to right
What does it REALLY mean?
Add & Subtract
4 + 5 or 10 - 2
Always complete left to right
In your groups, you solved this question:
3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2=
Review your work and make any changes you
would like……
3 + 2 x 2 x 2 x 2 x 2- 4 ÷ 2=
5
3+ 2
-4÷2
3 + 32 - 2
35 – 2 = 33
39 × (15 ÷ 3) – 16
(3 + 7) × 6 + 4
48 ÷ 8 + 5 × (7 – 2)
64 ÷ (15 – 7) × 2 – 9
13 × 4 – 72  8
100 
2
5
×
3
4
3
4
– 24  8
5 × 6 – (9 – 4)
4×
2
(5
– 12) – 6
13 +
3
(4
÷ 2) × 5 – 17
34 –
2
8
÷4
78 –
4
2
÷ (14 – 6) × 2