What is Division Before Addition (BODMAS)?

S1-SA1-0179

Grade Level:

Class 5

Maths, Computing, Programming, AI

Definition

What is it?

Division Before Addition is a rule within BODMAS (or PEMDAS) that tells us the order to solve mathematical problems. It means that whenever you see both division and addition in the same problem, you must always perform the division operation first, before doing any addition.

Simple Example

Quick Example

Imagine you have 10 laddoos and your friend gives you 2 more. Then you share 6 laddoos equally among 3 people. If you write this as 10 + 2 / 6, the rule says you first divide 2 by 6, which doesn't make sense for laddoos. But if you mean (10 + 2) laddoos, then divide by 6, that's different. The rule helps us know the right order to get the correct answer.

Worked Example

Step-by-Step

Let's solve: 15 + 6 / 3

Step 1: Identify the operations. We have addition (+) and division (/).
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Step 2: According to BODMAS, division comes before addition. So, we solve the division part first.
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Step 3: Perform the division: 6 / 3 = 2.
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Step 4: Now, replace the division part with its result in the original problem: 15 + 2.
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Step 5: Perform the addition: 15 + 2 = 17.
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Answer: 17

Why It Matters

Understanding this order is super important for solving complex math problems correctly, whether you're calculating scores in a cricket match or planning a budget. In computing and programming, computers follow these exact rules to perform calculations, ensuring programs like those used in AI or data analysis give accurate results.

Common Mistakes

MISTAKE: Adding numbers first because they appear first in the problem. For example, in 10 + 4 / 2, doing 10 + 4 = 14, then 14 / 2 = 7. | CORRECTION: Always look for division (and multiplication) first, even if it's not at the beginning. In 10 + 4 / 2, first do 4 / 2 = 2, then 10 + 2 = 12.

MISTAKE: Ignoring the rule completely and solving from left to right for all operations. | CORRECTION: Remember BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) is a strict order. Division and Multiplication have higher priority than Addition and Subtraction.

MISTAKE: Confusing division with multiplication's priority. | CORRECTION: Division and Multiplication have the same priority. You solve them from left to right in the order they appear. However, both come before Addition and Subtraction.

Practice Questions

Try It Yourself

QUESTION: Solve: 20 + 10 / 5 | ANSWER: 22

QUESTION: A bus travels 30 km, then stops. After that, it travels another 15 km, but this distance is covered in 3 equal parts. What is the total distance effectively covered if you add the first 30 km and one part of the 15 km journey? (Solve: 30 + 15 / 3) | ANSWER: 35

QUESTION: Solve: 5 + 20 / 4 + 7 | ANSWER: 17

MCQ

Quick Quiz

Which operation should you perform first in the expression: 12 + 8 / 4 - 2?

Addition

Subtraction

Division

It doesn't matter

The Correct Answer Is:

According to BODMAS, division (8 / 4) has a higher priority than addition (12 + 8) and subtraction (4 - 2). So, division should be done first.

Real World Connection

In the Real World

When calculating your monthly mobile bill, if there's a base charge of ₹199 and then an extra data charge of ₹50 for every 10 GB used, you might see a calculation like 199 + 100 / 10. Your mobile company's billing system uses BODMAS to correctly calculate that you used 100 GB (100/10 = 10 extra units), so your bill is 199 + (100/10) = 199 + 10 = ₹209.

Key Vocabulary

Key Terms

BODMAS: An acronym for the order of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction) | Operation: A mathematical process like addition, subtraction, multiplication, or division | Priority: The order in which operations should be performed | Expression: A mathematical phrase that can contain numbers, variables, and operations

What's Next

What to Learn Next

Great job understanding this! Next, you should learn about 'Multiplication Before Addition' within BODMAS. It's similar to division's priority and will help you solve even more complex problems accurately.