The rules for ordering operations refers to set rules that are used to give a convention about what procedures need to be performed first and in what order so that mathematical expressions can be evaluated. This convention is known as PEMDAS. It is an acronym where P stands for parenthesis, E is for exponents, M for multiplication, and D is division, A for addition, and S stands for subtraction. Another acronym that is widely used depending upon the region is called BODMAS (Brackets, order, division and multiplication, addition and subtraction). Now let us take a look at why we require this ordering of operations.
Issue 1
Suppose you are given a mathematical expression such as 10 + 2 * 4. There are two ways to solve this question. We could either perform addition first and then multiplication. This gives the answer.
(10 + 2) * 4 = 12 * 4 = 48.
Another way to solve this problem is by performing multiplication first and then addition. So we have
10 + (2 * 4) = 10 + 8 = 18
So the question that arises is what is the correct way to solve this expression in order to get the right answer?
We could say that the answer depends on a persons perspective; however, mathematics does not work like that. We do not have that kind of flexibility to not be sure of the correct answer in math. To combat this confusion, mathematicians came up with the rules for ordering operations. According to PEMDAS, we have first to apply multiplication and then addition. Hence, the second option where we get the answer 18 is correct.
Issue 2
The acronym PEMDAS can be misleading in some cases. Multiplication and division hold the same rank while Addition and Subtraction also hold the same rank. If you have a mathematical expression that consists of only multiplication and division, the problem that arises is which operator needs to be applied first. Suppose we have the mathematical expression 10 / 2 * 5. Once again, we have two ways to solve this problem
(10 / 2) * 5 = 5 * 5 = 25
Or,
10 / (2 * 5) = 10 / 10 = 1
How do we decide which is the correct solution? The answer is simple: we move from left to right. The operation that comes first is the one that we will perform at the beginning of our calculations. Hence, in this case, solution 1 that yields 25 as the answer is correct. Next, we look at addition and subtraction. Suppose our expression is 10 – 3 + 2; the solutions are given as follows.
- Solution 1: (10 – 3) + 2 = 7 + 2 = 9
- Solution 2: 10 – (3 + 2) = 10 – 5 = 5
In this case, too, we work from left to right, and solution 1, which gives the answer 9, is correct.
How to Study PEMDAS?
As this topic can prove to be very confusing, it will serve a student well to join an online coaching institute such as Cuemath. The math experts at Cuemath use a vast plethora of resources such as online worksheets, workbooks, math games, and puzzles to explain concepts to young minds. They focus on building a strong mathematical foundation and encourage kids to achieve their best while having fun. Overall, they provide a holistic learning environment that promotes flexibility and logical thinking amongst children of all ages.
Conclusion
Mathematics is not a subject that you must approach with fear; instead, learn mathematics with curiosity, and the world will be your oyster. Hopefully, this article helps you to clear your concepts of PEMDAS, and I wish you all the best!
