basics of simplification for SSC UPSC IBPS

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Simplification

Step 1: Parts of the expression enclosed in ‘Brackets’ must be solved first. Inside the brackets, once again BODMAS rules apply!
Step  2: The mathematical operators ‘of’ and ‘order’ must be solved next. ‘Of’ means part of and is solved by substituting with a multiplication sign. ‘Order’ is the same as exponent. Powers are solved after brackets. Powers also include roots.
Step 3: Next, the parts of the equation that contain ‘Division’ and ‘Multiplication’ are calculated.
Step 4: Last but not least, the parts of the equation that contain ‘Addition’ and ‘Subtraction’ should be calculated.
Here is an example, to help you understand the BODMAS rule concept.

What will come in place of question mark (?) in the following question?
240 ÷ 8 × 512 ÷ 4 + ½ of {1800 ÷ (11 × 24 ÷ 8 × 3 – 69)2} = ?
(1) 4111
(2) 3441
(3) 4441
(4) 3841
Ans: (4)
Solution:
Given expression is,
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.

Now, Try It Yourself:
Que. 1
What will come in place of question mark (?) in the following question?
24 + 13 – 5 × ½ of 10 - {45 ÷ (17 – 2)} =?

1.
11
2.
-7
3.
9
4.
18

Solution

Follow BODMAS rule to solve this question:
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.
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