BODMAS rule

It gives us an order in which to perform the mathematical operations in a given problem or equation. It is actually an acronym and goes as follows

This is the order in which you perform the operations to arrive at the correct answer. You first solve the operations within the bracket. This is called “opening the bracket’. Then you move on to division, after which you perform multiplication if the equation requires it from left to right. And finally, you add the numbers and lastly perform the subtraction.

The best way to understand the BODMAS rule is through examples.

Given expression is,

24 + 13 – 5 × ½ of 10 – {45 ÷ (17 – 2)} =?

⇒ ? = 24 + 13 – 5 × ½ of 10 – {45 ÷ (15)}

⇒ ? = 24 + 13 – 5 × ½ of 10 – {3}

⇒ ? = 24 + 13 – 5 × (½ × 10) – 3      (of means ‘×’)

⇒ ? = 24 + 13 – 5 × 5 – 3

⇒ ? = 24 + 13 – 25 – 3

⇒ ? = 9

Hence, the required answer is 9.

240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ (11 × 24 ÷ 8 × 3 – 69)2} = ?

According to the BODMAS, first we need to solve the Brackets.

Here in this equation first we will solve curly bracket and inside the bracket, we will again follow BODMAS Rule. In the curly bracket once again another bracket appears. So we solve that bracket first. Within these smaller brackets, there is no ‘of’ or ‘order’, so we proceed with the following steps in BODMAS.

We see multiplication, division and subtraction signs. Since multiplication and division are of the same rank, we go left to right to solve this. First we multiply, then we divide. Then we perform the second multiplication. After that, we proceed to the subtraction.

Here are the steps to illuminate this process.

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ (264 ÷ 8 × 3 – 69)2} = ?

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ (33 × 3 – 69)2} = ?

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ (99 – 69)2} = ?

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ 302} = ?

Now we have reached the end of the small brackets. We encounter our first exponent. So we need to solve this ahead of division.

Now solving curly bracket,

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ 900} = ?

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ of 2 = ?

So far we have cleared all the brackets. Now we move to the next step. We come across our first ‘of’. Here, we simply treat ‘of’ as product i.e. multiplication. But note that, ‘of’ will be solved before a regular multiplication.

⇒ 240 ÷ 8 × 512 ÷ 4 + ½ × 2 = ?

⇒ 240 ÷ 8 × 512 ÷ 4 + 1 = ?

Now, we have cleared our expression of all brackets, exponents and ‘of’s. We now move to the 3rd step. Here we perform all the divisions and multiplications. Note that these two operations are the same rank. So we perform either in the order we come across them in, from left to right.

⇒ 30 × 512 ÷ 4 + 1 = ?

⇒ 15360 ÷ 4 + 1 = ?

⇒ 3840 + 1 = ?

Now we have cleared the expression of all multiplication and division operations as well. All we are left with is addition and subtraction.

⇒ ? = 3841

Hence, the required answer is 3841.