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Math Order of Operations: BODMAS rule (i.e PEMDAS rule)

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The concept of order of operations in algebra lessons is one of the very basic concepts that the student must understand well, because this concept forms a basic base for all algebra lessons that will study later.

The arithmetic operations we encounter have addition, subtraction, multiplication and division (the four operations) combined or not in the same algebraic expression.

In other cases we find in the same algebraic expression in addition to the four operations, powers and grouping symbols(brackets), which will inevitably affect the change of priority of operations(BODMAS rule).

So what is BODMAS rule?

Bodmas' rule is a method for performing a series of arithmetic operations in an algebraic expression without errors. The meaning of these letters is:

  • B: Brackets (Grouping symbols);
  • O: Order (Exponent, square root, factorial);
  • D: Division (/);
  • M: Multiplication (*);
  • A: Addition (+);
  • S: Subtraction (-);

Note:

Another synonym for PODMAS rule is PEMDAS rule, which means the same thing, the order of operations in math. The reason for changing some letters is due to several labels for the same concept. These are the meanings of the letters of the word PEMDAS:

  • P: Parentheses (Grouping symbols);
  • E: Exponent (Exponent, square root, factorial);
  • M: Multiplication (*);
  • D: Division (/);
  • A: Addition (+);
  • S: Subtraction (-);

When evaluating expressions, proceed in the following rules order.

Note:

  1. Evaluate expressions contained in grouping symbols first(BOMDAS). If grouping symbols are nested, evaluate the expression in the innermost pair of grouping symbols first.
  2. Evaluate all exponents that appear in the expression(BOMDAS).
  3. Perform all multiplications and divisions in the order that they appear in the expression, moving left to right(BOMDAS).
  4. Perform all additions and subtractions in the order that they appear in the expression, moving left to right(BOMDAS).

These are some special cases in the order of operations.

Note:

  • Multiplication and division are the same importance.
  • Addition and subtraction are the same importance.

Let's take some examples to see the order in which the arithmetic operations are performed. These examples will be from simpler to complex.

Example1:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression has only addition and subtraction (they have the same precedence), so we proceed from left to right.

Example2:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression has only multiplication and division (they have the same precedence), so we proceed from left to right.

Example3:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression is combined by three operations: addition, subtraction and multiplication. So, we perform the multiplication first, Then, we accomplish the operation from left to right.

Example4:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression is combined by three operations: addition, division and multiplication, and parentheses So, we perform what is inside the parentheses first(Priority is for the division first).

Example5:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression is combined by three operations: addition, division and multiplication, and parentheses and barckets So, we perform what is inside the Brackets first(Priority is for what inside the parentheses).

Example6:

calculate numerical expression below using the rules of Order of Operations.

Solution:

This expression is combined by three operations: addition, division and multiplication, and parentheses and powers So, we powers inside the parentheses first.