BODMAS Rule

BODMAS is an abbreviation that helps remember the sequence of steps followed when solving mathematical expressions. The word BODMAS stands for:

• B = Brackets ( )
• O = Order (powers or roots)
• D = Division (÷)
• M = Multiplication (×)
• A = Addition (+)
• S = Subtraction (-)

This rule states that if a given expression has multiple operators, they must be performed from left to right by following the rule. It means that brackets should be solved first, then the powers of roots, division or multiplication, and finally addition or subtraction.

Division and multiplication are performed from left to right, depending on which appears first, as they have equal precedence.

Let us take an example to get a better understanding of the BODMAS rule. 

Solve \(25 ÷ 5 × 2 + 2^2 - (4 + 5)\)

\(25 ÷ 5 × 2 + 2^2 - 9\) (brackets: (4 + 5))
\(5 × 2 + 2^2- 9\) (division: 25 ÷ 5)
\(10 + 2^2 - 9 \)(multiplication: 5 × 2)
14 - 9 (addition: 10 + 4)
5 (Subtraction: 14 - 9)
 

BODMAS, PEMDAS, and BIDMAS are acronyms that help recall the correct order of mathematical operations in expressions that have multiple operators. 

 

These terms help solve complex problems accurately. Parentheses group expressions and must be solved first. Exponents, also called indices, are the same as powers, which indicate the number of times a number is repeatedly multiplied by itself. 

Mathematical operations are the basic arithmetic operations we perform on numbers. The four main operations in BODMAS are:
 

• Addition (+): Solve addition from left to right. 
   
• Subtraction (-): Solve subtraction from left to right. 
   
• Multiplication (×): Solve multiplication from left to right.
   
• Division (÷): Solve division from left to right. 
  
  
   

The pattern of the operations in BODMAS is:
 

1. First, solve the brackets. 
    
2. Solve the powers, square roots, and other exponents.
    
3. Then division and multiplication.
    
4. Followed by addition and subtraction. 

These rules are used for systematic calculation of all the mathematical operations. The rule reduces the chances of misinterpretation of various operators. For example, if the given expression is \( 6 + 4 × 2\). If we do not follow the BODMAS rule, it will result in an incorrect answer.  
\(6 + (4 × 2)\)


According to the BODMAS rule, multiplication comes before addition. Therefore, the multiplication problem must be resolved first:

First, solve the brackets: \(4 × 2 = 8\)
Then, solve the addition:\( 6 + 8 = 14 \)

If we perform mathematical operations differently, the answers will be incorrect. The BODMAS rule maintains consistency and ensures everyone gets the correct answer. 
 

The simple tips and tricks that should be kept in mind while dealing with the BODMAS rule are:
 

• Solve the brackets first, then follow the exponents. Perform division or multiplication, then addition or subtraction from left to right. 
   
• Use parentheses to break down complicated expressions and ensure accuracy in the answers. For example, if the given expression is \((12 ÷ 2) × 5\).
  \((12 ÷ 2) × 5 = 6 × 5 = 30\).
   
• Practice the BODMAS rule and expressions with multiple operators daily to build a proper understanding of the concept. 
   
• Perform division or multiplication as well as addition or subtraction from left to right to avoid mistakes. 
   
• Double-check each step by estimating the result to ensure you haven’t skipped any operation or misapplied the order.

Learning the concept and properties of the BODMAS rule plays a vital role in our daily lives and makes complex mathematical calculations easier. The practical uses of the BODMAS rule are listed below:

Shopping and billing: Calculating total costs with discounts, taxes, and offers requires applying BODMAS to get the correct bill.
 

Cooking and recipes: Adjusting ingredient quantities in complex recipes with fractions and multipliers involves using BODMAS for accurate measurements.
 

Construction and engineering: Solving expressions in measurements, areas, and volumes requires BODMAS to ensure precise calculations.
 

Finance and budgeting: Calculating interest, loan payments, or splitting expenses often involves multiple operations, where BODMAS ensures accurate results.
 

Science experiments: Measurements, formulas, and data analysis in experiments often require BODMAS to correctly perform calculations and interpret results.