[ad_1]
If you are studying for your upcoming Armed Services Vocational Aptitude Battery or ASVAB exam, you will be required to know many different mathematical formulas and calculations, all of which will have to be completed without the use of a calculator. In this article I will cover one very important topic to help you with your mathematical questions. And this is the approach to knowing and properly understanding the laws and the orders of operation.
There are a number of different mnemonics that you can use to remember what comes first in a mathematical equation. The two most common ones are
Please Excuse My Dear Aunt Sally
and PEMDAS which literally is P-E-M-D-A-S.
Both of these give you the rules that tell you the order of operations in a mixed mathematical equation and the order is as follows:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Typically you proceed in the order of the operations given. Parenthesis is always first and exponents always second. However, multiplication and division can be seen as a set. That means if multiplication or division comes first, it does not matter which one you do first as long as you place them in the correct order.
The same concept applies to addition and subtraction. As long as these are completed last within your series of operations, it doesn’t matter if you add or subtract first.
Some people are confused by this concept that says that you can do multiplication and division in any order, same with addition and subtraction. You can think of this as being the same thing and if you can understand this concept, it will make sense and you will have an easier time doing mathematical equations.
When you divide a number by another number, you are essentially doing the same thing. For example, if I have the equation that says 4 times a half. When I write this out, I have 4 times 1 divided by 2. Four times 1 over 2 can actually be seen as 4 times 1 and both of them divided by 2. Four times 1 is 4 and therefore my equation actually says 4 divided by 2. So multiplying by a fraction is dividing by a number.
Now if I gave it to you the other way, for example I give you 3 divided by 7, you can look at this equation instead as being read 3 times 1 over 7. If you can understand that the multiplication and division are essentially the same idea, you will understand why the order between these two doesn’t matter.
Same applies for addition and subtraction. If I have an equation that reads 3 minus 7, the equation is really telling me to do 3 plus negative 7. Same applies if I have a positive value. If I have something like 4 plus 3, this really means 4 minus negative 3. Given that two negatives cancel out making it a positive, so once again the operations are essentially the same thing and therefore their individual orders don’t matter.
[ad_2]