What is Pemdas Rule and How Did it Originate?

Most of us have solved many mathematical operations using the PEMDAS rule. You might have wondered how this rule of Mathematics came into being. We are here to discuss how the PEMDAS rule originated and continues to evolve. We need this rule in our everyday life for simple mathematical calculations that we come across. Many scientific and graphing calculators follow the rule of PEMDAS.

PEMDAS is an abbreviation for the order of operations that needs to be followed while solving a mathematical operation. It stands for, P – Parenthesis, E – Exponents, D – Division, M – Multiplication, A – Addition, and S – Subtraction. One of the easiest ways to memorize this abbreviation is with the help of a mnemonic- “Please Excuse My Dear Aunt Sally”. Codes written in any of the programming languages are based on this rule on a basic level.

Role of Order of Operations in PEMDAS Rule

Order of Operations is a specified sequence according to which mathematical operations are performed. PEMDAS rules follow the order of operations. This simply means that operators starting from the left will be solved first followed by the second till the last operator, which is subtraction. If the order of operations is violated, you might get a wrong answer. It is also important because it guarantees that people around the world will decipher and solve any mathematical operation in the same manner.

How Did it Originate?

There is no such solid evidence of a particular person inventing it. The rules of order of operations have grown over hundreds of years and still continue to evolve till date. We will discuss how some of the mathematical events during the course of history shaped PEMDAS into a rule that we follow today.

1. During the 1600s, the need for mathematical convention arose. At that time, the rule that multiplication has precedence over addition appeared to have arisen naturally and nobody disagreed with this fact. Thus, it was accepted as an algebraic idea and was developed by mathematicians of that era. The distributive property implies a natural hierarchy in which multiplication is considered to be more powerful than the operator addition. Thus, people having different conventions also couldn’t argue this fact.
2. By the onset of the 1800s, the text “order of operations” started to appear in the school textbooks and students started using it. It was used more by students than by mathematicians. Mathematicians only discussed it and did not make anything official.
3. Many suspect that the concept of the order of operations and the abbreviation PEMDAS, was developed only in the 1900s or at least in the late 1800s.
4. In the 1920s, the mathematicians started to discuss whether multiplication should take precedence over division, or whether it should be treated equally. Mathematician, Florian Cajori, pointed out that there were many disagreements. Although many would still argue who won this argument, today it has become most common that division and multiplication are equal starting from left to right. The general rule is that Parenthesis should be used to clarify the meaning, which is prevalent till date.
5. As mathematicians started to write books on mathematics starting from the 1960s, algebraic notation that multiplication would take precedence over addition was agreed upon by all. The natural rule that multiplication has precedence over addition was present from the very beginning of the notation, and probably, it existed already, though in a different form, in the geometric or the verbal forms of expression that existed before algebra became a language. The artificial rules such as equal precedence for multiplication and division or the left to right evaluation did not have any absolute reason for their acceptance. They had to be accepted and till date continue to flourish.

If you want to know more about the rule of PEMDAS and the order of operations, do visit Cuemath to know it in an interesting way.