Rules related to Simplification / Approximation

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 mutiplication 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

Some questions of simplification

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 - 17⁴ – 13⁴ – [- 52(17)³ – 68(13³)] = (?)*221

1) 1432

2) 1326

3) 1450

4) 1567

5) 1234

Using formula: (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³+ b⁴) 
⇒ (a – b)⁴ - a⁴ + 4a³b + 4ab³ - b⁴ = + 6a²b² 
(17 -13)⁴ - 17⁴ – 13⁴ – [- 52(17)³ – 68(13³)] = (?)*221 
Here, a = 17 and b = 13 
⇒ (?)= (6 (17)² (13)²)/221 
⇒ (?) = (6 × 289 × 169)/221 
⇒ (?) = 1326

Option 2 is correct

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

1. 1000
2. 1020
3. 1040
4. 1080
5. 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

1. 270
2. 280
3. 290
4. 300
5. 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)/(7²-8*6+a²) = 1

1. 1
2. 5
3. 9
4. 13
5. 17

    Solution: Using the BODMAS rule

                (8*a – 14)/(49-48+a²) = 1

                (8*a – 14)/(1 + a²) = 1

                8a – 14 = 1 + a²

                a² – 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

1. 400
2. 450
3. 550
4. 600
5. 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

1. 189
2. 107
3. 174
4. 296
5. 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:

• 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.