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Question 135200: Useing the PEMEDS expesssion, (Please, excuse, my dear, aunt sally)
Simplify
1. 2+3*5^2-7
2. 6+3[(12/4)+5]
3. (4/2)+4(5-2)^2
4. -8-81/9*2^2+7
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Useing the PEMEDS expesssion, (Please, excuse, my dear, aunt sally)
Simplify
1. 2+3*5^2-7 = 2+3*25-7 = 2+6-7 = 1
----------------------------
2. 6+3[(12/4)+5] = 6+3[3+5] = 6+3*8 = 6+24 = 30
------------------------------
3. (4/2)+4(5-2)^2
(1/2) + 4(3)^2
(1/2) + 4*9
(1/2) + 36
36 1/2
----------------
4. -8-81/9*2^2+7
= -8-9*4+7
= -8-36+7
= -37
====================
Cheers,
Stan H.
Answer by Edwin McCravy(20059)  (Show Source):
You can put this solution on YOUR website!
Stanbon's problems #1 and #3 are incorrect.
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Solution by Edwin:
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In doing PE(MD)(AS) problems, the important things are:
1. Do ONLY ONE operation on each step.
2. After doing an operation, copy everything else over.
3. Do NOT skip steps.
4. You must begin inside the innermost set of parentheses.
Brackets are considered as parentheses.
5. After doing a step, start completely over with PEMDAS.
6. Remember that Multiplication is not necessarily done before
Division and Divison is not necessarily done before multiplication.
We go entirely by which one is first going left to right.
7. Remember that Addition is not necessarily done before
Subtraction and Subtraction is not necessarily done before
addition. We go entirely by which one is first going left to right.
8. Any time there is more than one operation of the same kind, always
do the one which comes first going left to right.
1.
2+3*5^2-7
P is for PARENTHESES. Go to the first PARENTHESIS going left to right
There are no PARENTHESES.
Look for EXPONENTS. We find the first ^ going left to right. I
will color it and the numbers on each side of it red:
2+3*5^2-7
So replace the 5^2 by 25
So now we have
2+3*25-7
or
2+3*25-7
Now we start over.
P is for PARENTHESES. Go to the first PARENTHESIS going left to right
There are no PARENTHESES.
E is for EXPONENTS. Go to the first EXPONENT going left to right
There are no EXPONENTS.
M and D are for MULTIPLICATION and DIVISION. Go to the first
MULTIPLICATION or DIVISION going left to right. I will color it and the
numbers on each side of it red:
2+3*25-7
So replace the 3*25 by 75
So now we have
2+75-7
or
2+75-7
Now we start over.
P is for PARENTHESES. Go to the first PARENTHESIS going left to right
There are no PARENTHESES.
E is for EXPONENTS. Go to the first EXPONENT going left to right
There are no EXPONENTS.
M and D are for MULTIPLICATION and DIVISION. Go to the first
MULTIPLICATION or DIVISION going left to right.
There are no MULTIPLICATIONS or DIVISIONS.
A and S are for ADDITION and SUBTRACTION. Go to the first
ADDITION or SUBTRACTION going left to right. I will color it
and the numbers on each side of it red:
2+75-7
Now replace 2+75 by 77
and now we have
77-7
and since there is just one thing to do, we subtract and get
70
------------------------------------------------------
2.
6+3[(12/4)+5]
P is for PARENTHESES. Go to the first PARENTHESIS going left to right.
So we find the first parentheses going left to right. They are the
brackets. Brackets are considered as parentheses. I will color the
bracket and its contents blue:
6+3[(12/4)+5]
Now we must work only inside the blue brackets until there is nothing in
there left to do.
Now we start over inside the blue brackets only:
P is for PARENTHESES. Go to the first PARENTHESIS inside the blue
brackets going left to right. So we find the first parentheses going
left to right. I will color the parentheses and its contents red:
6+3[(12/4)+5]
There is only one thing to do inside the red parentheses and that is
to divide 12 by 4, so we replace (12/4) by
(3) and we can drop the parentheses since
there is just one number inside it and it is not used to indicate
multiplication. So we just replace it by 3.
6+3[3+5]
or just
6+3[3+5]
Now there is just one thing to do inside the blue brackets and that is
to replace the [3+5] by [8]. Notice that we MAY NOT drop the blue brackets because they are
used to indicate multiplication. So we have
6+3[8]
Now we start over.
6+3[8]
P is for PARENTHESES. There is a bracket, but it contains nothing to
do inside it.
E is for EXPONENTS. There are no EXPONENTS.
M and D are for MULTIPLICATION and DIVISION. There is one
multiplication, 3[8]. So we replace 3[8] by 24 and get
6+24
So there is just one thing to do, and that is to add 6+24, and
so the final answer is
30.
-----------------------------
3. (4/2)+4(5-2)^2
(4/2)+4(5-2)^2
(4/2)+4(5-2)^2
2+4(5-2)^2
2+4(5-2)^2
2+4(5-2)^2
2+4(3)^2
2+4(3)^2
2+4(3)^2
2+4(9)
2+36
38
-------------------------------------------
4. -8-81/9*2^2+7
-8-81/9*2^2+7
-8-81/9*4+7
-8-81/9*4+7
-8-81/9*4+7
-8-9*4+7
-8-9*4+7
-8-9*4+7
-8-36+7
-8-36+7
-8-36+7
-44+7
-37
Edwin
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