Current Status

Not Enrolled

Price

Free

Get Started

Success Bureau

Smart Learning

India's Premier Institute for NRA CET

B O D M A S

Bracket , Of , Division , Multiplication & Addition

Bracket, of, Division, Multiplication & Addition

[ , ( ) , of , ÷ , x , + , ─ , ]

For the simplification of the expressions which involves signs brackets, of, ÷, x, +, ─ , the rule of ‘BODMAS’ should be strictly followed .

In the word ‘BODMAS’ each letter is the initial letter of a word :

B Stands for Bracket

O Stands for of ( i.e. ‘multiplication’ )

D Stands for Division

M Stands for Multiplication

A Stands for Addition

S Stands for Subtraction

Note : The order from the Left hand side should be strictly maintained .

Besides, you should follow the following rule while solving such questions :

Rule 1 : If an expression Contains brackets, the expression within the brackets should be simplified first.

Rule 2 : If an expression contains ‘Of’, multiplication, division, addition and subtraction, then of should be performed first then followed by multiplication or division.

Proceeding from left to right, addition and subtraction are carried out in the order in which the sign of addition and subtraction are given.

If expression contains ‘Of’ and Division – always do ‘Of’ and then do division

Rule 3 : If expression involves all the four operations,then multiplication and division is carried out first in the order in which they are given from left to right. The same rules are carried out for addition and subtraction

Examples :

Q.1 2 + 5 ÷ 5 = ?

Solution : 2 + 5 ÷ 5 = 2 + 1 = 3 ( correct answer ) and Not 2 + 5 ÷ 5 = 7 ÷ 5 = 7 / 5 ( wrong answer )

Q.2 9 + 8 of 2 – 4 + 23 = ?

Solution : 9 + 16 ─ 4 + 23 = 48 ─ 4 = 44 ( ‘of’ = ‘multiplication’ )

Bracket Rules :

(i) Before opening any bracket first solve the figures inside the bracket .

(ii) Brackets are in the following order :

Ist ( IInd , IIIrd ( ivth )

( iii ) The opening of the brackets should start from the ivth order .

(iv)If there is no sign before bracket it means Multiplication .

Note : If there is -ve sign before bracket , it will change all the signs within the bracket .

Q.3 Simplify, 1.2 x 1.5 + 1.2 x 2.5 + 1.2 x 3

Solution : 1.2 x (1.5 + 2.5 + 3 ) = 1.2 x ( 7 ) = 8.4

Q.4 Simplify, 3.5 x 3.5 – 2 x 3.5 x 2.5 + 2.5 x 2.5

Solution : We know that a² – 2ab + b² = ( a- b )²

Hence , ( 3.5 – 2.5 )² = 1² = 1

Q. 5 Simplify ( 1/2 + 1/4 ) of 16

Solution : (1/2+1/4) of 16

Step 1: While Solving the fraction inside the bracket first add

1/2 + 1/4 = 3 / 4

Step 2: Now the expression will be 3 / 4 of 16 =

3/4 × 16 = 12

Simplification of Brackets

Simplification of brackets in an expression means expansion of brackets. We can remove brackets from an expression by expanding them by multiplication. We should use Distributive Law of Multiplication ove Addition or Multiplication .

We can write it as :

Note : The order of brackets to be simplified is (), {}, [] .

Q.6 : Simplify, 9 ( 5 + 3 ) .

Solution :

(i) The terms inside the bracket are like terms. We can solve this by two methods.

Method 1: Add the terms inside the bracket and multiply the number outside bracket with the sum.

Method 2: Multiply the number outside the bracket with each term inside the bracket and add the products.

9 ( 5 + 3 ) = ( 9 x 5 ) + ( 9 x 3 ) = 45 +27 = 72 .

Q 7 : Simplify , 11 ( 2x + 3 )

Solution :

Here , you can notice that the terms are unlike.

This can be simplified by multiplying the number outside the bracket with the terms inside the bracket and add the products .

11 ( 2x – 3 ) = ( 11 x 2x ) + ( 11 x 3 ) = 22x + 33

Q 8 : Simplify , 1800 ÷ 10 { ( 12 – 6 ) } + ( 24 – 12 ) }

Solution :

Step 1: Simplify the terms inside {} .

Step 2: Simplify {} and operate with terms outside the bracket .

1800 ÷ 10( 12−6 )+( 24−12 )

1800 ÷ 10{ 6+12 } ⇒ 180 { 18 } = 3240

Q. 9 : Simplify , 1/2 [{−2 ( 1 + 2 ) } 10 ]

Step 1: Simplify the terms inside () followed by {} , then [] .

Step 2: Now, Operate terms with the terms outside the bracket .

1/2 [ { −2 ( 1 + 2 ) } 10 ]

= 1/2 [ { -2 ( 3 ) } 10 ]

= 1/2 [ { -6 } 10 ]

= 1/2 [ -60 ] = – 30

Major Rules to Follow

CONDITIONS	RULES
X + ( Y + Z ) => X + Y + Z	Open the bracket and add the terms .
X - ( Y + Z ) => X - Y - Z	Open the bracket and multiply the negative sign with each term inside the bracket . ( All positive terms will be negative and vice-versa ) .
X ( Y + Z ) => XY + XZ	Multiply term outside with each term inside the bracket .

Types of Questions on Simplification

There are two possible ways to ask a question which is related to simplification. Simplification question will take place in all important competitive exam because we can check the individual analytical thinking through the simplification.

Finding the missing number from the calculation will be the First type of simplification. In this type to get solution approximate the given number or we can simplify using the basic operations.
The second Method will understand the relation between the numbers and simplify the numbers using the rules of simplification.

Important Questions

Q. 1 (10.8×16×12) + (3.6×56×9.2) =?

3941.35
3966.89
3928.32
3649.19
3645.19

Answer : 3
Solution:

Even + Even should be always Even. So the unit digit should be in even.
Note: All numbers should be Even.

Q. 2 12.3% of 203 + 23% of 1110 =?

270.269
240.269
280.269
290.269
None of these

Answer : 3
Solution :

Tricks : A% of B = B % of A

3/4
5/7
3/7
4/7
None of these

Answer : 2
Solution:

Q.4 3545 ×14.75 – 2325 ×15.25 =?

15369.5
16832.5
11546.5
12475.5
None of these

Answer : 2
Solution:
1220×15 – 5870 ×0.25 = 16832.5
(15+0.25=15.25; 15-0.25=14.75) (a-b , a+b)
Here,
3545+2325=5870 (x+y)
3545– 2325 =1220 (x-y)

Q.5 27% of 250 +22% of 920 +21% of 660=?

419.5
423.5
408.5
415.5
None of these

Answer : 3
Solution:
Common percentage method:
(250+920+660) =1830
Here 20% is common;
20% of 1830 =366
Further,
1^st part (20+7) = 7% of 250 =17.5
2^nd part (20+2) = 2% of 920 =18.4
3^rd part (20+1) = 1% 660 = 6.6
366+17.5+18.4+6.6 = 408.5

Q.6 21² +17²-13²= ?

412
512
561
461
None of these

Answer : 3
Solution:
Method :
21² +(17² -13²) = 21² +((17+13)(17-13)) = 441 +(30×4) =561
Note: (A² – B²⁾ = (a+b) (a-b)

Q.7 (22×28) + (38×42) = ?

2122
2212
2132
2213
None of these

Answer : 2

Note: If any two numbers in multiplication with common base number, we can use this method

Q.8 12.75 % of 464 = ?

59.96
57.16
51.86
59.16
None of these

Answer : 4
Solution :
(12.75×4) of (464/4) = 51% of 116 =59.16
Note : If any fractional number ends with 5 , we can convert that into whole number by this method .

Q.9 8.2% of 780 +x= 12.9% of 1310

107.26
106.53
105.03
103.56
None of these

Answer : 3
Solution:
82×78/100 + X =129×131 /100
(130-1)(130+1) /100 – (80+2)(80-2) /100 =X
X=105.03
Q. 10 0.875 of 848 + 0.625 of 624= ?

1132
1325
1236
1250
None of these

Answer : 1
Solution:
87.5% of 848 + 62.5% of 624
(7/8 ×848) + 5/8 ×624 = 742 +390 =1132
Note: 87.5% = (100-12.5)%
= (1-1/8) =7/8

Practice Questions with Solutions

Q. 1 1035 ÷ [(3/4) of (71 + 65) – 15 ¾] = ?

12
24
18
26
None of these

Answer : 1

Solution :

1035 ÷ [(3/4)*136 – 63/4] = x

X = 1035 ÷ [102 – (63/4)]

X = 1035 ÷ [(408 – 63)/4]

X = 1035 ÷ (345/4)

X = 1035 *4/345

X = 12

Q. 2 (7 × 7)³ ÷ (49 × 7)³ × (2401)² = 7^?

7
5
6
8
None of these

Answer : 2

Solution :

(7 × 7)³ ÷ (49 × 7)³ × (2401)² = 7^x

(7²)³ ÷ (7² × 7)³ × (7⁴)² = 7^x

7⁶ ÷ 7⁹ × 7⁸ = 7^x

7^{6 – 9 + 8}= 7^x

7⁵ = 7^x

X = 5

Q. 3 √((27 ÷ 5 ×?) ÷ 15) = 5.4 ÷ 6 +0.3

12
4
9
15
None of these

Answer : 2

Solution :

√((27 /5 )×(x/15)) =0.9+0.3

(3/5) √ x = 1.2

√ x = 6/3 =2

X= 4

Q. 4 5 ¾ – 4 1/8 + 7 ½ – 3 3/8 = ?

4 3/7
6 5/6
7 ½
5 ¾
None of these

Answer : 4

Solution :

5 ¾ – 4 1/8 + 7 ½ – 3 3/8 = x

X = (5 – 4 + 7 – 3) (3/4 – 1/8 + ½ – 3/8)

X = 5 [(6 – 1 + 4 – 3)/8]

X = 5 (6/8) = 5 (3/4)

Q. 5 36³ × 4096^1/2 × 72 × 18 ÷ (9³ × 72²) = 4^?

8
12
7
5
None of these

Answer : 4

Solution :

(36*36*36*64*72*18)/(9*9*9*72*72) = 4^x

4*4*4³ = 4^x

4⁵ = 4^x

X = 5

Q. 6 (2 7/9) ÷ (5 1/2) × (693/350) = (1/3) of (5/7) of (147/175) of (?)

Answer : 3

Solution :

(25/9)*(2/11)*(693/350) = (1/3)*(5/7)*(147/175)*x

1 = (x/5)

X = 5

Q. 7 (913 + 329 + 522 + 343) ÷ (18 + 24 – ? + 18) = 43

Answer : 2

Solution :

(913 + 329 + 522 + 343) ÷ (18 + 24 – x + 18) = 43

2107 ÷ (60 –x) = 43

(2107/43) = 60 – x

49 = 60 – x

X = 60 – 49 = 11

Q. 8 (3/7) of ? – (2/5) of (13/16) of 2160 = 12 % of 900

2150
1540
1960
1890
2370

Answer : 4

Solution :

(3/7)*x – (2/5)*(13/16)*2160 = (12/100)*900

(3x/7) – 702 = 108

(3x/7) = 108 + 702

(3x/7) = 810

X = (810*7/3) = 1890

Q. 9 12 ¾ % of 2400 + 23 ½ % of 800 + 45² = 1125 ÷ 25 × 4 + ?

Answer : 3

Solution :

(51/400)*2400 + (47/200)*800 + 2025 = (1125/25) + 4x

306 + 818 + 2025 – 45 = 4x

3104 = 4x

X = 3104/4 = 776

Q. 10 ∛157464 + √8836 – 45 % of 800 =? + (1188 ÷ 9) – 36²

952
816
878
924
None of these

Answer a

Explanation:

54 + 94 – (45/100)*800 = x + (1188/9) – 1296

54 + 94 – 360 + 1296 = x + 132

54 + 94 – 360 + 1296 – 132 = x

X = 952

Q. 11 (4/5) of 11325 + 56 % of 1750 = (?)² + 436

Answer : 3

Solution :

(4/5)*11325 + (56/100)*1750 = x² + 436

9060 + 980 – 436 = x²

10040 – 436 = x²

9604 = x²

X = 98

Q. 12 (4/5) of 11325 + 56 % of 1750 = (?)² + 436

Answer : 3

Solution :

(4/5)*11325 + (56/100)*1750 = x² + 436

9060 + 980 – 436 = x²

10040 – 436 = x²

9604 = x²

X = 98

Q. 13 1.8 × 625 + 5.6 ÷ 0.7 + 415 × 11.8 = (?)² – 211

Answer : 1

Solution :

1.8 × 625 + 5.6 ÷ 0.7 + 415 × 11.8 = (?)² – 211

1125 + 8 + 4897 = x² – 211

6241 = x²

X = 79

Q. 14 18 ¼ % of 17200 + 33 2/3 % of 1860 + 37 2/3 % of 19680 = ?

11178
13456
9824
10242
8454

Answer : 1

Solution :

(73/400)*17200 + (101/300)*1860 + (113/300)*19680= x

X = 3139 + 626.2 + 7412.8

X = 11178

Q. 15 586 × 9234 ÷ 48 % of 950 = 36 × 750 ÷ 4 + ? + 4500 .

Answer : 3

Solution :

586 × [9234 ÷ ((48/100)*950)] = 36 × (750/4) + x + 4500

586*(9234/456) = 6750 + x + 4500

11866.5 – 11250

X = 616.5

Q. 16 1323 ÷ (27 % of 700) = 35 × 7 3/5 of (? ÷ 190)

Answer : 4

Solution :

1323 ÷ [(27/100)*700] = 35 × (38/5)*(x/190)

1323 ÷ 189 = 35 × (38/5)*(x/190)

(7*5*190)/(35*38) = x

X = 5

Q. 17 (28 × 9 + 54 × 3 + 12 × 11) ÷ (14² – √961 + 17) = ?

Answer : 2

Solution :

(28 × 9 + 54 × 3 + 12 × 11) ÷ (14² – √961 + 17) = x

X = (252 + 162 + 132) ÷ (196 – 31 + 17)

X = 546/182

X = 3

Q. 18 32450 ÷ 11 + (4/9) of 11520 + 48 % of 7500 = ?² – 430

150
178
110
92
None of these

Answer : 3

Solution :

(32450/11) + (4/9)*11520 + (48/100)*7500 = x² – 430

2950 + 5120 + 3600 + 430 = x²

X² = 12100

X = 110

Q. 1 9 √13225 + ∛205379 + 52 % of 700 = 408 + ?

156
218
189
130
None of these

Answer : 4

Solution :

√13225 + ∛205379 + 52 % of 700 = 408 + x

115 + 59 + (52/100)*700 – 408 = x

115 + 59 + 364 – 408 = x

X = 130

Q. 20 49² ÷ 14 × 8 + 58² = 4 × ? – 15 % of 2480

1489
1277
1645
1823
None of these

Answer : 2

Solution :

(49*49*8)/14 + 58² = 4x – (15/100)*2480

1372 + 3364 = 4x – 372

1372 + 3364 + 372 = 4x

5108 = 4x

X = 5108/4 = 1277

Dear Student , You are advised to sincerely Learn the Study Material and attempt all the Online Quizzes / Mock Tests to ensure your success in the forthcoming Competitive Examination. The Study Material includes such questions as are often asked in the Actual Examination .