Dealing with the basic math operations is inevitable even for those subjects and cases that are not directly related to engineering or programming. University students majoring in MBA, Sociology, Banking, and Political Science, among other subjects, also have to do their calculations. Therefore, it is vital to learn mathematical operations starting from the most basic cases and train one’s brain to achieve automation.
For example, multiplication and addition have certain arithmetic properties. These are associative (it represents two or more occurrences of addition or multiplication alone as the operands are not changed), commutative (order of the operands doesn’t change the result), distributive (it combines addition and multiplication), inverse (additive inverse), and identity-based (an element that leaves other elements unchanged in combination) properties.
Order of Operations in Mathematics
The majority of college students these days find it quite challenging to understand the order of mathematical operations. They have learned it wrong as schoolchildren or faced too much fear of dealing with the numbers or various problems. Starting with the Parentheses, Exponents, Multiplication, and Division, it is often considered that multiplication comes first and only division follows later or that addition must come before subtraction, which is incorrect.
Order of operation rules states that:
– Parentheses have primary importance. Focus on the purpose and role of each element or approach them as separate packages as you work with some calculations.
– Exponents should come next.
– Here is where multiplication and division parts should start. There is no clear priority when you have a specific consecutive string as these must be done from left to right except for some equations with reverse thinking.
– Contrary to popular belief, addition and subtraction must come as the final point and consecutive strings must be approached left to right as well.
Remember that when you must deal with more than one operation at the same level regarding the existing order of operations, you must move from left to right.
Note that IF we have no Parentheses or Exponents, we move to Multiplication and Division aspects. It makes understanding the order of math operations essential even for simple tasks or when using four-function calculators that may approach evaluation with a left-to-right approach. It should be checked manually to avoid mistakes.
List of Mathematical Operations
Currently, we have five basic operations in Math that include addition, subtraction, multiplication, division, and modular forms like the Holomorphic function or Fourier series.
While it is not possible to list all mathematical operations that include modulation or relate to Physics with all their odd mathematical symbols, learning certain rules in Algebra must be learned at greater depth.
- Commutative Property
It speaks of equations in which the order of given numbers does not affect an outcome. Commutative operations in Math are multiplication and addition.
7+4 = 4+7 = 11
3*2 = 2*3 = 5
We turn to basic math primary school examples to show how it works in practice, not to provide an unresolved Math problem.
- Associative Property
It deals with equations where we must use the grouping of the numbers. They do not affect our final result. Just like commutative operation, addition and multiplication here represent associative operations.
(1+4) + 5 = 4 + (1+5) = 10
(1*3) * 2 = 3 * (2*1) = 6
Remember that subtraction and division are not associative. While these are basic arithmetic operations, it is vital to understand them as you proceed with more complex tasks.
- Distributive Property
It can be implemented when the sum of two quantities is multiplied by a third quantity
(2+5) * 3 = 2 * 3 + 5 * 3 = 21
- Negative Numbers
In addition to that, a basic list of mathematical operations also includes work with negative numbers. The rules state that you must calculate the sum, difference, product, and quotient of negative whole numbers.
- The addition of two negative numbers results in a negative.
- Adding a positive and negative number results in a number that has the same sign as the number of some larger magnitude.
- Dealing with subtraction of a positive number, we shall receive the same result as the addition of a negative number of equal magnitude.
- Subtracting a negative number results in the same scenario as adding a positive number.
- The product of a single positive number and one negative number is negative.
- Product of two negative numbers is positive.
- Finally, the quotient of one positive number that we have and a single negative number is, as a rule, negative. The quotient of two negative numbers is positive.
- An underlying principle of addition states that two debts (negative numbers) can be combined into a single debt that has a greater magnitude.