If you are here that means you know all the operations within indices as well as their properties. You have learned how to do a single operation but what if you are given more than one operation in just a single equation? Would to perform the addition operation first or product operation at the last? That is why in this lesson you will learn how to tackle equation that consists of more than one mathematical operation.

BODMAS Rule

When you are given an equation to solve which contains more than one mathematical operation then you need to use the BODMAS rule to solve your equation. BODMAS is basically an order of performing mathematical operations to get the right answer. Without the BODMAS rule, people will be getting different answers and the truth is they didn't do anything wrong. For example, three students were given an equation which is: 14 - (3 + 5 \times 2)

Student 1 solved it in this way:

14 - (3 + 10)

14 - 13

1

Student 2 solved in this way:

14 - (8 \times 2)

14 - 16

-2

And student 3 solved in this way:

14 - 3 - 5 \times 2

6 \times 2

12

Did you notice something? None of the students made any error but yet they are getting different answers. Which one will you say is correct? It will be unfair to other students since they also did it correctly. That is why we use the BODMAS rule to find the same solution. BODMAS is an acronym. The BO in BODMAS stands for Bracket Off. The in BODMAS stands for Division. The M in BODMAS stands for Multiplication. The A in BODMAS stands for Addition. Last but not least, S stands for Subtraction. You can also call it the hierarchy of operations. Through BODMAS, you can judge any solution since everyone will get the same answer. If you don't know how to use the BODMAS rule then don't worry, below are the steps to use the BODMAS rule.

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Hierarchy of the Operations

1. Brackets Off

For example, your teacher asked you to solve this equation: 4/2 + (2 - 3 \times 2) + (14 / 2). Of course, your teacher won't write to use the BOMDAS rule because there is no other way to solve indices except using the BODMAS rule. The first thing you need to do is to remove brackets. To remove brackets, you need to do the mathematical operations within the bracket. It doesn't matter whether it is addition, division, or any kind of mathematical operation, just solve it so that you can remove the brackets. In simple words, carry out the operations in parentheses, brackets, and braces.

4/2 + (2 - 6) + 7

4/2 + (-4) + 7

4/2 - 4 + 7 (Be careful with the minus sign)

2. Division

The next step is to apply the division operation. In the above example, if you check carefully, a division operation is been applied to the first term. Solve it.

4/2 - 4 + 7

2 - 4 + 7

3. Multiplication

Once you applied the division operation, now you need to multiply. In the above example, there is no multiplication operation hence we can skip to the next step. Don't get worried if you see any operation missing in your equation, just skip to the next step in the BODMAS rule.

4. Addition

Now it's time to apply the addition operation. In the above example, you can see the plus sign meaning we need to apply addition operation.

2 - 4 + 7

9 - 4

5. Subtraction

Last but not least, you will be left with subtraction operation. Apply it.

9 - 4

5

And that is how you solve indices using the BODMAS rule. Since you know how to use the BODMAS rule, why don't you check the above three student's solutions and let us know which is one correct and why?

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.