Why is it important to follow the order of operations? What are some possible outcomes when the order of operations is ignored? If you invented a new notation where the order of operations was made clear, what would you do to make it clear?

In mathematics , the order of operation also known as precedence rule is a rule used to clarify which procedures should be performed first in a given mathematical expression. When there is more than one operation involved in a mathematical problem, it must be solved by using the correct order of operations. The rules are 1. Calculations must be done from left to right. 2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first ie starting our work with the innermost pair, moving outward. 3. Exponents (or radicals) must be done next.

4. Multiplication and division are done next .
5. Addition and subtraction must be done next.
The acronym which can be used to remember this order is
Big Elephants Destroy Mice And Snails (Brackets, Exponents, Divide, Multiply, Add, Subtract) If the order of operation is not followed, a lot of problem is created. we get different answers for the same problem. for example 15 + 5 X 10 -- Without following the correct order, we know that 15+5=20 multiplied by 10 gives me the answer of 200. 15 + 5 X 10 -- Following the order of operations, we know that 5X10 = 50 plus 15 = 65. This is the correct answer, where as the above is wrong. If I was to invent a new notation where the order of operation was made clear, I would have used colours. I would have assigned each operator a colour.

...September 20, 2005
Dear Student,
The Order of Operations is not one of the hardest, nor is it one of the easiest things that you will have to learn in Algebra and other mathematical classes. To begin in learning the Order of Operations, you must follow the steps, hence the "order" of the operation. To start off, the first step would be to do anything that is inside of grouping symbols ([ ], ( ), { }). Next you would have to do powers from the left to the right (9 squared). Following the Order of Operations, the next phase of a problem would be to do all of the multiplication and division from the left to the right (*, /). The final stage in the Order of Operations is to do all of the addition and subtraction from the left to the right (+, -). Now, you just have to finish by putting it altogether and finding the answer.
Example-
3*6(35-3+5)10squared
1) First do
anything inside 3*6*37*10squared
grouping symbols.
2) Next you do powers 3*6*37*100
from left to right.
3) Now multiplication 66,600
and division from the
left to the right.
4) Lastly you would do
addition and subtraction
but this problem doesn't
have any.
Above is an example of how the Order of Operations works. It should always be done this way. An example of someone doing it the wrong way is...

...The Order of operations
Part I-Teach someone else
Dear Friend,
I've gotten wind of your predicament concerning things such as: The Order of Operations, what they are, and all of their facets, among a few other things. I believe I can help you out with this, and took the liberty of explaining a few things concerning the aspects of the Order of Operations in the following parts of this letter.
A) What Operation Symbols Do You Know ?
The Operation Symbols that are needed for a person to be familiar with are Muliplication, Division, Addition, and Subtraction.
B) What Grouping Symbols Do You Know ?
The Grouping Symbols that you are needed to know are the parenthesis and the brackets.
C) What is the "Order of Operations" ?
The Order of Operations consists of (in a nutshell): Multiplication, Division, Addition, and Subtraction (in that specific order). This can be mentally compressed into "My Dear Aunt Sally".
D) Why is the "Order of Operations" Important ?
The Order of Operations is important because, without it, we would have no definite shape or way of how to formulate answers and relate them to each other on a consistent basis.
E) What is the order of use for the grouping symbols ?
You must remember to...

...Order of operations is a rule to clarify confusion that may occur in an equation that has multiple different operations. This rule of Order of Operations states we must solve a complex equation by complete the operations in this order: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. We can remember this by this mnemonic: Pink, Eyes, May, Doubt, Anyone’s, Style.
*** This will happen if we take this equation and NOT follow the Order of Operation***
4+ 2 x 3 =
If I did not know the “rule” I would assume that I’d complete the problem this way
4 + 2= 6 x3 = 18 “oops I forgot my PEMDAS rule”
Let’s try this again:
4+ 2 x 3= okay I need to multiply first so I’ll fix this so I know what needs to be done first
4+ (2 x 3) = Ah ha! I get it now!
4+ (2x3) = 4+6 =
10!!!!!
Okay now….Lets make this harder!
42x 10+6-9=_____
I remember the rules by using PEMDAS which means I need to start with the ( ) first
42=2 x 10+6-9=____
Next I use the multiplication
2x10=20+6-9=____
Now since addition and subtraction are interchangeable, I can do either one. I’ll keep it simple:
26-9=17
Put it all together and you will have
(42)x 10+6-9=17
Well that’s great…but what if I don’t wanna use that rule? Lets find out!
42x 10+6-9=_____
Lets add the 10 and the 6 first…….which gives me
42x 16-9=____
Now let’s subtract...

...was proven and tested that area of contact does not affect the coefficient of friction. Based on data, area doesn’t affect much the value of the coefficient of friction since the values just differ in minimal aspects
It is strictly necessary to observe uniform motion through constant speed in order to have a constant value for the coefficient of friction. Coefficient of friction in general definition, where a body moves in equilibrium or in constant speed or motion, kinetic friction is essentially constant. According to the 1st Law of motion by Isaac Newton, if an object experiences no net force, then its velocity is constant. Therefore summations of forces in the vertical and horizontal are zero. By that we can then compute for the coefficient of friction.
CONCLUSION
Friction has a lot of applications in our daily life. It is friction in the tires that allows the car to stay on road and friction in the clutch that makes it possible to drive at all. The coefficient of friction on a block remains constant when the block travels in uniform motion. Since friction is in the direction opposite of the net force, the net force should always increase when the mass of the block increase in order for the block to overcome its state of inertia. A body travelling on an inclined plane due to its weight has an angle of repose, wherein it has a uniform sliding motion. There is no acceleration taking place when the block slides uniformly. No matter what...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...Assignment 1: Number and Operations
. . . Math 1901 .
1.
−3 + 2 =
a. The temperature in the morning when you leave to come to school is -3 degrees. When the sun comes out, the temperature warms up by 2 degrees. What is the temperature after the sun comes out?
1 0 -1 -2 So by moving up 2 degrees, we see that we end up at -1 degrees. -3 To solve this problem, start by finding -3 degrees on our thermometer/ number line. We know from before, that when we are adding numbers, we move up the number line.
-3 + 2 = -1
-4 Morning temp Rise in temp
b. A frog is sitting on the stairs, on the 3rd step down from the main floor. It jumps up 2 steps. Which step is it on now?
Main Floor -1 step -2 step -3 step -4 step -5 step So by having our frog jump up 2 steps, we see that we end up on 1 step below the main floor, or -1. To solve this problem, start by putting our frog on the 3rd step down from the main floor (-3). We know from before, that when we are adding numbers, we move up the number line, or in this case the stairs.
-3 + 2 = -1
2.
5 − (−3) =
a. Black tokens are positive numbers, red tokens are negative numbers. There are 5 black tokens in the cup. I want to take out 3 red tokens. How many tokens are left in the cup? I have no red (negative) tokens in my cup, so I need to add some. By adding some, that changes how many I have altogether, so I need to balance the numbers and make it so that I am adding “0”. By adding 3...

...Order of operations is the order in which to evaluate different operations.
The order of operations is critical to solving different algebraic problems. Without it people will get different answers when there is no right one because there is no correct order to interpret an expression.
In order of operations you evaluate from left to right
in the followingorder
You may remember this as "Please excuse my dear Aunt Sally"
Parentheses
Exponents
Multiplication & Division
Addition & Subtraction
Remember with parentheses you solve the innermost first when there is a parentheses within one and within another or whatever, after that you can then simplify the second innermost grouping symbol.
Using parentheses you can change the order when you want something different.
Multiplication does not always come before division and addition does not always come before subtraction.
For example if you have a expression like 8 ¸ 4 x 7 - 5 + 3
Since multiplication & division comes first you solve 8 ¸ 4 x 7
Which we end up with 2 x 7. If you had done multiplication first you would have ended up with 8 ¸ 28 which is wrong!...

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