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What is the full form of BODMAS

BODMAS: Bracket, of, Division, Multiplication, Addition and Subtraction

BODMAS stands for Bracket, of, Division, Multiplication, Addition, and Subtraction. It refers to the order of operations to solve an expression. It is also known as the Bodmas rule, which tells which process to perform first to evaluate a given numerical expression. It is also known as PEDMAS - Parentheses, Exponents, Division, Multiplication, Addition and Subtraction.

BODMAS Full Form

Brackets → ( or ) ← Parenthesis

Order → √ or X2 Exponents

Division → ÷ or ÷ ← Division

Multiplication → × or × ← Multiplication

Addition → + or + ← Addition

Subtraction → - or - ← Subtraction

It is easy to solve a basic summation which has two numbers and one single operation, such as addition, subtraction, multiplication, or division. But if there are many numbers and different operations in an expression then how will you decide from where to start and which operation to perform first, which to perform second and third and so on? For such expressions, we need BODMAS, as it clears the confusion and tells us the right sequence of operations: Division, Multiplication, Addition, and Subtraction.

For example:

20 x 5 + 40/2 = ?

Using the BODMAS rule, in the above expression, first, we need to perform division, followed by multiplication, and then addition. Such as:

  • 40 / 2 = 20
  • 20 x 5 = 100
  • 100 + 20 = 120, so the answer is 120

Conditions to adhere to:

  • Open any brackets if there are any, then add or remove the terms. The formulas x + (y + z) = x + y + z and z + (y - z) = z + y - z
  • If there comes any minus sign before a bracket, then simply change the signs inside the bracket and solve further after removing that bracket. x - (y + z) ⇒ x - y - z
  • Multiply the term just outside the bracket by each term within if one or more terms are present. x(y + z) ⇒ xy + xz

Common Mistakes with Reference to the BODMAS Rule

The following are some frequent mistakes that can be made while using the BODMAS rule to simplify expressions:

  • Multiple brackets may confuse people, which could lead to us receiving the incorrect response. Since there are many different types of brackets in an expression, it is possible to solve all of the same types of brackets at once.
  • Incorrect knowledge of integer addition and subtraction can lead to errors in some situations. As an illustration, 1-3+4 = -2+4 = 2. But occasionally, mistakes like 1-3+4 =1-7 = -6 are made that result in the incorrect answer.
  • Making the assumption that division comes before multiplication and addition come before subtraction is incorrect.
  • Regardless of whatever occurs first in the statement, addition and subtraction must be performed after multiplication and division since they are same-level operations and must also be completed in the left-to-right order. As D comes before M in BODMAS, one may get the incorrect result if they solve division first before multiplication (which is on the left side of the multiplication operation).

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