Simplification generally means to find an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.

Simplification questions are asked in the exam to check the ability of an aspirant to deal with numbers which can be in one of the following two types.

- Sometimes, a calculation is given and one of the numbers is missing from the calculation. To find out the missing number, we have to approximate the given numbers or do the basic operations.
- Sometimes all the numbers are given with some operations between them & we have to simplify the calculation.

__Rules related to Simplification__

__Rules related to Simplification__

**Rule-(I) Replace ‘of’ by ‘Multiplication’ & ‘/’ by ‘Division’.**

**Explanation: **Whenever we find ‘of’ in a simplification problem, we can replace that by ‘multiplication(*)’. Similarly ‘/’ can be replaced by ‘÷’.

__Example:__** Find ¼ of 20**

**Solution:** (¼) x 20 = 20÷4 = 5

**Rule-(II)**** ****Always keep in mind the “BODMAS” rule. These operations have priorities in the same order as mentioned.**

**Explanation: **Whenever we have more than one operation in the given calculation, we have to do the operations according to the priority specified by ‘BODMAS’

- B-Bracket
- O-Of (means multiplication)
- D-Division
- M-Multiplication
- A-Addition
- S-Subtraction

__Example:__ Simplify: (2+3)*30

**Solution:** In this question, we have two things-Bracket & Multiplication. According to the BODMAS rule, we have to solve bracket first and not multiplication. So now coming to bracket, we have only one operation-Addition, so we will do addition.

(2+3)*30 = 5*30

Now we have only one operation to do – Multiplication

5*30 = 150

__Example__: Simplify: (2+5) of 80

**Solution:** In this question, we have three things – bracket, addition & of. Replacing ‘of’ by ‘multiplication’.

(2+5) of 30 = (2+5)*80

Now we have three things – bracket, addition & Multiplication. According to the BODMAS rule, we have to solve bracket first and not multiplication. So now coming to bracket, we have only one operation-Addition, we will do addition.

(2+5)*80 = 7*80

Now we will do multiplication.

7*80 = 560

**Rule-(III) Multiplication & Division have the same priority(Do that operation first which is on left)**

**Explanation: **Though division has more priority than multiplication according to ‘BODMAS’ but we can perform any of the two operations first if multiplication is on left.

__Example__: 8*30/15

8*30 ÷ 15

**Solution:** In this question, we have two things – Multiplication & Division. Multiplication is on left So we can perform that first.

Doing Multiplication first:

240 ÷ 15

16

Doing division first:

8*2

16

**Rule-(IV) Addition & Subtraction have the same priority.**

**Explanation: **Though addition has more priority than division according to ‘BODMAS’ but we can perform any of the two operations first.

__Example__:** 30+40-15**

**Solution:** In this question, we have two things – Addition & Subtraction. So we can perform any operation first as they have same priority.

Doing Addition first:

70 – 15

55

Doing Subtraction first:

30 + 25

55

**Rule-(V) ****Don’t hesitate in rounding the numbers to nearest integers.**

**Explanation: **Most of the times the numbers are given in such a way that you can round them quickly and get the answer (Rounding should be done or not, It can be realised by looking at the given options).

__Example__**: (324.5*15)/(5.01*24.98)**

**Solution:** (325*15)/(5*25)

=13*3

=39

Now let us see some of the previous year questions asked from 'Simplification' & try to apply the rules learnt so far.

**Q. 1) (17 -13) ^{4} - 17^{4} – 13^{4} – [- 52(17)^{3} – 68(13^{3})] = (?)*221**

Using formula: (a – b)^{4} = a^{4} – 4a^{3}b + 6a^{2}b^{2} – 4ab^{3}+ b^{4})

⇒ (a – b)^{4} - a^{4} + 4a^{3}b + 4ab^{3} - b^{4} = + 6a^{2}b^{2}

(17 -13)^{4} - 17^{4} – 13^{4} – [- 52(17)^{3} – 68(13^{3})] = (?)*221

Here, a = 17 and b = 13

⇒ (?)= (6 (17)^{2} (13)^{2})/221

⇒ (?) = (6 × 289 × 169)/221

⇒ (?) = 1326

**Q.2) Simplify: 127.001 * 7.998 + 6.05 * 4.001**

- 1000
- 1020
- 1040
- 1080
- None of these

**Solution:** Using the rounding concept

127 * 8 + 6 * 4

Using the BODMAS rule

1016 + 24

1040 (Option 3)

**Q.3) What will come at place of ?: 9876 ÷ 24.96 + 215.005 - ? = 309.99**

- 270
- 280
- 290
- 300
- 310

**Solution:** Using the rounding concept

9875 ÷ 25 + 215 - ? = 310

Using the BODMAS rule

395 + 215 - ? = 310

610 - ? = 310

? = 300 (Option 4)

**Q.4) What will come at place of a: (128 ÷ 16 x a – 7*2)/(7 ^{2}-8*6+a^{2}) = 1**

- 1
- 5
- 9
- 13
- 17

**Solution:** Using the BODMAS rule

(8*a – 14)/(49-48+a^{2}) = 1

(8*a – 14)/(1 + a^{2}) = 1

8a – 14 = 1 + a^{2}

a^{2 }– 8a + 15 = 0

a=3 or 5 (Option 2)

**Q.5) What will come at place of ?: 85.147 + 34.192*6.2 + ? = 802.293**

- 400
- 450
- 550
- 600
- 500

**Solution:** Using the rounding concept

85 + 35*6 + ? = 803

Using the BODMAS rule

85 + 210 + ? = 803

295 + ? = 803

? = 508 [approx. = 500] (Option 5)

**Q.6) What will come at place of ? : (3/8 of 168)*15 ÷ 5 + ? = 549 ÷ 9 + 235**

- 189
- 107
- 174
- 296
- None of these

**Solution:** Using the BODMAS rule

(3*168÷8)*15 ÷ 5 + ? = 549 ÷ 9 + 235

(504÷8)*3 + ? = 61 + 235

63*3 + ? = 296

189 + ? = 296

? = 107 (Option 2)

__Key points to remember while solving Simplification Question:__

__Key points to remember while solving Simplification Question:__

- Replace ‘of’ by ‘Multiplication’
- Replace ‘/’ by ‘Division’
- Always do the operations in priority according to ‘BODMAS’
- Division & Multiplication have the same priority (Start from left)
- Addition & Subtraction have the same priority
- Rounding can be done to simplify problems
- When the given options are very close then rounding doesn’t help much
- Always look at the options before doing simplification that can help in the elimination of options.

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