When we talk about general equations which contain brackets, people find it difficult to solve them. This might be due to the reason that they are not aware of the proper sequence of solving those equations.
For solving such expressions, we have a concept of order of operations in mathematics. The PEMDAS rule states first that we need to compute the expressions in the parentheses. PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
All these operations need to perform in the above-mentioned sequence only as it will help you get your answer in a very short period & that too correctly. When we see the concept of PEMDAS, a second preference is given to order i.e. Exponents. These are the powers of a given number. After solving the exponents, all the other mathematical operations are carried out.
What is PEMDAS?
This acronym is a contraction of Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. In some regions, it is called BODMAS (Brackets, Order, Division, Multiplication, Addition, and Subtraction).
PEMDAS is just like BODMAS, the only difference is in the sequence of operations. While the division is done first in the case of BODMAS, Multiplication is given first preference in PEMDAS. Rest all the operations are the same in both cases. So, whichever you choose, the answer will always remain the same.
Order for solving expressions through PEMDAS:
For solving any mathematical expression, the PEMDAS rule needs to be applied to get the right solution. Following is the correct way of solving any expression of maths:
- Parentheses: If you are given any expression with parentheses in it, then the first thing you need to do is to solve those brackets () in the correct sequence. If you don’t do it correctly, you won’t get the right answer.
- Exponents: Here order doesn’t refer to the sequence, but the exponents, roots, squares etc. that are included in the expression. After removing/solving all the brackets, you need to start with solving the exponents or other mathematical figures.
- Multiplication: Once all the brackets & orders are solved, the first mathematical operation that you need to do is multiplication. It should be given the first preference before any other mathematical operations.
- Division: After you divide, you are left with a small number of numbers. And the ones which are left need to be divided accordingly as mentioned in the question.
- Addition: One of the easiest and the most favourite mathematical operations of all time. The addition of numbers is required to be done once division & multiplication have been carried out.
- Subtraction: Last operation and step for solving expressions with brackets are Subtraction. It is the least preferred operation while solving expressions.
Example of the order of operations:
Problem: 8 + (2 x 5) x 34 ÷ 9
Step 1 = 8 + 10 x 34 ÷ 9
(Removing the parentheses brackets by solving the expression inside the parentheses i.e. 2*5=10)
Step 2 = 8 + 10 x 81 ÷ 9
(After solving the parentheses, solve the exponents. In this case, it is 34= 81)
Step 3 = 8 + 810 ÷9
(Once the exponents are solved, start with the multiplication part as it is the third step in PEMDAS. Here, 10*81 is equal to 810)
Step 4 =8 + 90
(After multiplying the required numbers in the expression, you need to divide the specific ones according to the need of the expression. Like in this case, 810 ÷9= 90)
Step 5 = 98
(The last step of the order of operations in this question is added because we don’t have any subtraction in this case. So, here 8+90=98)
Therefore, our answer for the above operation is 98.
Order of operations is a very interesting concept in mathematics & it can be easily understood through the help of math experts, which you can easily find on Cuemath. These mentors can help you in understanding all the complex maths problems that cause worry to you.