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BODMAS Rule

BODMAS is an interesting mathematical concept that is used extensively to solve complex math problems. BODMAS helps you simplify questions and reduce your calculation time. The conceptual BODMAS questions for class 8 are generally seen in all competitive aptitude exams like the SAT, GMAT, and GRE. Thus, it becomes an important topic to learn. In this article, we will cover what BODMAS is, what problems are seen in exams, and how to solve them.

What is BODMAS?

ODMAS is a mathematical conceptual rule used to simplify a complex mathematical expression when you come around to a mathematical expression with multiple operations like addition, subtraction, division, or brackets.

For eg: 

(12+6×12+3)  (12+6×12+3)- What will you go first to solve? This problem is what the BODMAS rule solves.

Let’s start with  understanding what the BODMAS rule stands for. BODMAS rule is an abbreviation created to solve such complex math expressions.

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BODMAS Stands for

1. B stands for Bracket 
2. O stands for Order of Indices
3. D stands for Division
4. M stands for Multiplication
5. A stands for Addition
6. S stands for Subtraction

The line of follow-up on how the rule applies goes like this 

B→O→D→M→A→S

Brackets→Order of Indices→Division→Multiplication→Addition→Subtraction

The order of operations that we follow while applying the BODMAS rule is mentioned below:

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As we now understand the meaning of BODMAS, the full form, and the line of follow-up order, let us now understand the steps that we need to follow.

The steps we need to follow are :

To remember BODMAS, we have certain tips for you

Remember to solve BODMAS, the first thing is to make the expression simple. 

Then solve brackets by opening them, followed by the order of indices such as roots, and exponents, then move left to right by starting with division, multiplication, addition, and subtraction.

BODMAS and PEMDAS

The order of operations is followed from left to right. Both the rules are the same, just different abbreviations are used in different countries using different order.

When performing mathematical calculations, it’s crucial to follow a specific order to ensure accurate results. 

Two common acronyms, BODMAS and PEMDAS, outline this order. Both acronyms represent the same sequence: Parentheses, Exponents, Multiplication, and Division(from left to right), Addition and Subtraction (from left to right). The only distinction lies in the terminology used. BODMAS employs “Brackets” and “Orders,” while PEMDAS uses “Parentheses” and “Exponents.”

Both short-form abbreviations are used in the same way to solve the problems.

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When to use BODMAS in problems?

When you see a mathematical expression that has brackets and a lot of operations together, looking at the complexity of a problem, you can identify it as a BODMAS rule question.
The first thing to do is to open the brackets and make it a simpler equation. Once simplified, go according to the BODMAS law to solve the equation.Once done with simplifying the equation you will move from left to right and continue solving based on the order of operations in BODMAS.

Solving Questions using BODMAS Rule

Finally, now that you know all the basics let's get into real problem-solving questions.

• Question 1: 9+3x 8
  The correct answer is 9+24
  33
  The multiplication must be completed first (3x 8= 24) and then the addition 9+24 =33.
  This may be commonly miscalculated as 96 by working from left to right (9 + 3 = 12, 12 x 8 = 96).
• Question 2: 10x (24 + 6) + 7^2
  The correct answer is 10 x(30)+49
  349
  The BODMAS rule states we should calculate the Brackets first (24 +6= 30), then the Orders (72 = 49), then any Division or Multiplication (10 x 30=300, 30 is the answer to the brackets), and finally any Addition or Subtraction (300+ 49 = 349).

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• Question 3: 9– 6 + 5 ÷ 5
  The correct answer is 4.
  The division must be completed first (5/5=1) which then leaves addition and subtraction; as both are of the same importance, we can then work from left to right. 9– 6 + 1 (the answer to 5 ÷ 5) = 4.
• Question 4
  6(10+12÷3×4-6×1)
  Let's start with solving the inside of the bracket
  We shall start with division first 12÷3=4

            The equation now has become 6(10+4x4-6x1). Now multiplication 4x4=16, 6×1=6.

            The equation now has become 6(10+16-6)
            Now addition then subtraction
            =6(10+16-6)
            =6(26-6)
            =6(20)
            =120

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BODMAS

Simplifying Brackets In BODMAS

Understanding the distributive property is very important when you solve BODMAS questions. When we deal with mathematical expressions that involve brackets, distributive property comes into play.
This property states that:

• a(b + c) = ab + ac

In simpler terms, when we multiply a number or variable outside brackets by a sum or difference inside, it can be distributed to each term within the brackets.

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Applying the Distributive Property

Let's understand this by looking at a few examples:
Example 1:

Simplify: 8(6 + 2)

• Step 1: Distributing 8 to both terms inside the brackets:
  • 8 * 6 + 8 * 2
• Step 2:  Multiply:
  • 48 + 16
• Step 3: add like terms:
  • 64

Example 2:

Simplify: 3(4x - 5)

• Step 1: Distributing  3 to both numbers inside the brackets:
  • 3 * 4x - 3 * 5
• Step 2: Multiply:
  • 12x - 15

Remember when using BODMAS

• When you encounter expressions with brackets, always apply the distributive property just like in the questions we solved above.
• Remember to distribute the number or variable outside the brackets to each term inside the brackets.
• Combine like terms like adding similar variable terms after distribution to simplify the equation till we get an answer which cannot be solved further.
• By following these steps and understanding the distributive property, you can effectively simplify expressions involving brackets and confidently solve mathematical problems.

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Here are some problems for you to solve

1. Simplify: 42 - [35 - {18 - (12 - 8 - 4)}]
2. Evaluate: 9 + (12 - 5 × 3)
3. Simplify: 2/5 ÷ 4/7 × (8 + 10 × 4 - 3) + [3/8 ÷ 5/16 - {4/7 + 9/14}]
4. Determine the value of: 200 - [15 + {8 - (30 - 10)}]
5. Calculate: 3000 - [600 {320 - (100 - 90 + 80)}]
6. Evaluate: (20 × 19) ÷ 12 × 3 (3 + 14) - 35
7. Simplify: 2/3 [{ -3 (2 + 3) 12} 18] × 4
8. Determine the correct answer for (2/5 + 8/5) - 3
9. Solve: 3 [3 + 3 {42 - 3 (19 + 3)}]
10. Solve: 15 - [8 - {9 - (8 - 10 - 7)}]
11. Simplify: (4 + 4) × (4 ÷ 4) × (4 × 4)
12. Calculate: 2400 ÷ 12 {(15 - 8) + (36 - 18)}
13. Solve: 30 - [8 - {5 - (10 - 8 + 4)}]
14. According to BODMAS, find the value of y: 48 ÷ 3 + y × 4 - 30 = 12
15. Simplify: 60 × 4 × 8 × [25/5 + 48/12]
16. Solve using BODMAS: 3 [3 + 3 {42 - 3 (19 + 3)}]
17. Simplify: (32 - (-3) {7 - (8 - 4)}] ÷ [4 × {6 + (-4) × (-3)}]
18. Calculate: 25 - 1/25 {5+ 4 - (3+ 2- 1 + 3)}
19. Simplify: 42 - [35 - {18 - (12 - 8 - 4)}]
20. Evaluate: 65 - [30 + {45 - (30 - 7)}]

Now for your help, let’s solve some questions for you.

Answers

Problem1: Simplify: 42 - [35 - {18 - (12 - 8 - 4)}]

Step-by-Step Solution:

1. Innermost Brackets: Start with the innermost brackets:
   • 12 - 8 - 4 = 0
2. Continuing with Inner Brackets: Replace the innermost brackets with their result:
   • 18 - (0) = 18

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Moving to Outer Brackets: Replace the inner brackets with their result:

• 35 - {18} = 17

1. Final Calculation: Replace the outer brackets with their result:
   • 42 - 17 = 25

Therefore, the simplified expression is 25.

Problem 4: Determine the value of: 200 - [15 + {8 - (30 - 10)}]

Step-by-Step Solution:

1. Innermost Brackets: Start with the innermost brackets:
   • 30 - 10 = 20
2. Continuing with Inner Brackets: Replace the innermost brackets with their result:
   • 8 - 20 = -12
3. Moving to Outer Brackets: Replace the inner brackets with their result:
   • 15 + (-12) = 3
4. Final Calculation: Replace the outer brackets with their result:
   • 200 - 3 = 197

Therefore, the value of the expression is 197.

Problem 3: Simplify: 2/5 ÷ 4/7 × (8 + 10 × 4 - 3) + [3/8 ÷ 5/16 - {4/7 + 9/14}]

Step-by-Step Solution:

1. Innermost Brackets: Start with the innermost brackets:
   • 4/7 + 9/14 = 17/14
2. Continuing with Inner Brackets: Replace the innermost brackets with their result:
   • 3/8 ÷ 5/16 - 17/14 = 6/5 - 17/14 = 1/70
3. Moving to Outer Brackets: Replace the inner brackets with their result:
   • [1/70] = 1/70
4. Inner Parentheses: Simplify the expression within the parentheses:
   • 8 + 10 × 4 - 3 = 8 + 40 - 3 = 45
5. Division and Multiplication: Perform the division and multiplication:
   • 2/5 ÷ 4/7 × 45 = 2/5 × 7/4 × 45 = 63
6. Addition: Add the result to the previous calculation:
   • 63 + 1/70 = 4411/70

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Therefore, the simplified expression is 4411/70.

Problem 14: find the value of y: 48 ÷ 3 + y × 4 - 30 = 12
Solving for y:
Given equation: 48 ÷ 3 + y × 4 - 30 = 12

Step-by-Step Solution:

1. Division: Perform the division first:

   • 48 ÷ 3 = 16

2. Equation becomes: 16 + y × 4 - 30 = 12

3. Combine like terms:

   • 16 - 30 = -14

4. Equation becomes: -14 + y × 4 = 12

5. Isolate y: Add 14 to both sides:

   • y × 4 = 12 + 14

6. Simplify:

   • y × 4 = 26

7. Divide by 4:

   • y = 26 ÷ 4

8. Simplify:

   • y = 6.5

Therefore, the value of y is 6.5.

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Problem17: Simplify: (32 - (-3) {7 - (8 - 4)}] ÷ [4 × {6 + (-4) × (-3)}]

Step-by-Step Solution:

1. Innermost Brackets:
   • 8 - 4 = 4
2. Continuing with Inner Brackets:
   • 7 - 4 = 3
3. Moving to Outer Brackets:
   • (-3) × 3 = -9
4. Outer Brackets:
   • 32 - (-9) = 32 + 9 = 41
5. Inner Brackets:
   • (-4) × (-3) = 12
6. Outer Brackets:
   • 6 + 12 = 18
7. Division:
   • 41 ÷ 18 = 41/18

Therefore, the simplified expression is 41/18.

BODMAS Practice Questions for Class 4

Here are some BODMAS questions for Class 4:

1. (5 + 8) × 4 =
2. 7 + (24 ÷ 6 × 3) =
3. 15 - (3 × 4) =
4. (40 ÷ 8) - 5 =
5. (25 - 10) × (15 - 4) =
6. (10 - 7) + (4 × 6) =

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BODMAS Practice Questions for Class 5

Here are some BODMAS questions for Class 5:

1. 45 - 12 + 35 - (28 + 17) =
2. 52 - 10 + 45 + 32 - (35 + 18) =
3. 6 + 23 × 7 - (30 - 5) =
4. 8 + 27 × 9 - (36 - 6) × 2 =
5. (75 ÷ 3 - 5) × 4 + 8 =
6. (84 ÷ 4 - 7) × 5 + 9 × 2 =
7. 0.4 + 0.9 + 0.3 =
8. 40 + 40 × 0 + 2 =

BODMAS Practice Questions for Class 6

Here are some BODMAS questions for Class 6:

1. Solve the operation: 36 ÷ 6 + 7 (6 × 7)23 + 5 =
2. 42 ÷ 7 × (8 - 5) + 3 =
3. 5 - 3 + 4 + 8 × (20 ÷ 10) =
4. 7 × 3 + (14 + 9) - 24 ÷ 6 =
5. (15 - 9) × 4 + 10 + 32 - 4 =
6. (18 ÷ 3) + 5 + (20 - 11) × 5 =
7. 12 - 8 + 11 × 6 + 35 ÷ 5 =
8. 8 ÷ 4 + 30 - 27 ÷ 3 =
9. 5 + 3 × 24 ÷ 6 - 10 =

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FAQs about BODMAS

1. What does BODMAS stands for?

BODMAS is an acronym that stands for Brackets, Orders, Division and Multiplication, Addition, and Subtraction. It's a set of rules used to determine the order of operations in mathematical expressions.

2. Why is BODMAS important?

BODMAS ensures consistent and accurate results in mathematical calculations.By using BODMAS we can solve questions faster. It is also important that a student knows BODMAS as it comes in every competitive exam aptitude.

3. How do I use BODMAS?

Look for questions with complex equations, then start by moving left to right. Remember you follow the order of BODMAS -
B→O→D→M→A→S
Brackets→Order of Indices→Division→Multiplication→Addition→Subtraction
Solve any expressions within brackets first.
Once done with brackets, move to orders calculating exponents, roots, and powers. Now start with division and multiplication. At last, we have addition and subtraction. Make sure you perform these operations from left to right, whichever comes first.

4. What are some common mistakes people make with BODMAS?

One general mistake that students make while solving BODMAS questions is that - they do not follow the order: Performing operations in the wrong order can lead to incorrect results overall leading to the deduction of marks.

The second common mistake that students make is forgetting brackets. If brackets are present, always solve the expressions inside them first.

5. Can you give me an example of how BODMAS works?

Example: 10 + 20 ÷ 5 × 3 - 4

• We see there are neither brackets nor order like exponent, roots, or power in this expression.
• Only simple division and Multiplication: 20 ÷ 5 = 4, then 4 × 3 = 12.
•  And then addition and subtraction: 10 + 12 - 4 = 18.

Therefore, the answer is 18.

We hope that now after reading this article, you have become a pro at solving BODMAS rule questions. Keep visiting Global Tree for more such lessons and career-related queries, we provide you with the best solutions.