March 2, 2024

Simplification questions for class 6 with answers and practice questions with PDF

BODMAS rule simplification questions for class 6

The aim of simplification questions for class 6 is normally to evaluate a student’s ability with addition, subtraction, multiplication, and division. In these inquiries, complex expressions or equations must be made simpler by applying one or more operations to them.

The questions may involve the use of brackets or parentheses, exponents or indices, fractions, and decimals. Students may be asked to simplify expressions by combining like terms, factorising, or expanding.

Generally, simplification questions for class 6 are designed to assess a student’s learning of fundamental mathematical ideas . These questions play an important part in the growth of math ability and in building a foundation for future study of more difficult topics in the subject.

For simplifying an expression , the order of performing the various operations should be strictly in  the following order :

(i) Brackets               (ii) of        (iii) Division           (iv) Multiplication      (v) Addition        (vi) Subtraction

Remember the wordBODMAS ‘  , where the letters  B, O, D, M,  A,  S stand for Brackets , of,  Division,  Multiplication,  Addition  and  Subtraction  respectively. 

Simplification questions for class 6 with answers: 

(1) Simplify :      12-[20÷{8-2(9-5-2)}]

Sol.    12-[20÷{8-2(9-5-2)}]=  12-[20÷{8-2 x 2}]      (removing small brackets)

=12-[20÷{8-4}]

=12-[20÷4]                  (removing braces)

= 12-5                              (removing big brackets)

=7

(2)  4+4+4+4÷4

4+4+4+4÷4 =4+4+4+1                 (solving division)

=13

(3)    25− [4 + {16 − (12 − 2)}]

25− [4 + {16 − (12 − 2)}] =  25− [4 + {16 − 10}]                                    (removing small brackets)

= 25− [4 + 6]                                                 (removing curly braces)

=25-10                                                          (removing big brackets)

=15

(4)  36 − [18 − {14 − (15 − 4 ÷2 ×2)}] 

36 − [18 − {14 − (15 − 4 ÷2 ×2)}]= 36 − [18 − {14 − (15 − 2 ×2)}]                (Performing division  in small brackets)

=36 − [18 − {14 − (15 − 4)}]                       (performing multiplication)

= 36 − [18 − {14 − 11}]                       (removing small brackets)

=36- [18-3]                                              (removing curly braces)

=36-15                                                       (removing big brackets)

=21

(5)  10×10+[400÷{100-(50-\overline{3\times 10})}]

10×10+[400÷{100-(50-

\overline{3\times 10}
)}] =10×10+[400÷{100-(50-30)}]          (removing bar)

=10×10+[400÷{100-20}]                   (removing small brackets)

=10×10+[400÷80]                             (removing braces)

=10×10+5                                             (removing big brackets)

= 100+5                                                 (performing multiplication)

= 105

(6) 20[4+{16(12 3)}]

Sol.  20 – [4 + {16 – (12 – 3)}] = 20 – [4 + {16 – 9}]                        (Removing  small brackets)

= 20 – [4 + 7]                                    (Removing curly  brackets)

= 20 – 11                                           (Removing square brackets)

= 9

(7 ) 13-[20 ÷{8-2(9-5-2)}]

Sol. 13-[20 ÷{8-2(9-5-2)}]= 13-[20 ÷{8-2 x 2}]                 (removing small brackets)

=13-[20 ÷{8-4}]

=13-[20 ÷4]                                  (removing braces)

= 13-5                                             (removing big brackets)

=8

(8) [30 ÷ {10- (8- simplification questions)}]

Sol. [30 ÷ {10- (8- \overline{6-2}

)}] = [30 ÷ {10- (8- 4)}]                  (removing bar)

=[30 ÷ {10- 4}]                           (removing small brackets)

=[30 ÷ 6]                                      (removing braces)

=5                                                   (removing big brackets)

9) 10 + {8 + {5 + (2 + 3) – 6}}
Solution: 10 + {8 + {5 + (2 + 3) – 6}}=10 + {8 + {5 + 5 – 6}}                (Solving expression inside small bracket)
=10+{8+4}                                     (solving expression inside curly braces)
=10+12
= 22
Therefore  10 + {8 + {5 + (2 + 3) – 6}}= 22.

10) 15 – {10 – {6 – (2 + 1 ÷ 1)}} 
Solution: 15 – {10 – {6 – (2 + 1 ÷ 1)}}  = 15 – {10 – {6 – (2 + 1 )}}           (Solving division inside small bracket)
=15-{10-{6-3}}
=15- {10-3}                                   (solving expression inside curly braces)
= 15-7
=8
Therefore 15 – {10 – {6 – (2 + 1 ÷ 1)}}=8

11) 12 + {20 – {2 × (4 + 1)}}
Solution: 12 + {20 – {2 × (4 + 1)}} =12 + {20 – {2 × 5}}
=12 + {20 – 10}
=12+10
= 22
Therefore 12 + {20 – {2 × (4 + 1)}} =22

 12) 45 – {24 + {3 × (4 – 2)}}
Solution: 45 – {24 + {3 × (4 – 2)}} = 45 – {24 + {3 × 2}}
=45 – {24 + 6}
=45-30
= 15
Therefore   45 – {24 + {3 × (4 – 2)}} =15

13) 21 + {9 – {2 × (5 – 2) + 1}} 
Solution: 21 + {9 – {2 × (5 – 2) + 1}} =21 + {9 – {2 × 3 + 1}}
=21+{9-{6+1}}
=21+{9-7}
=21 + 2
= 23
Therefore 21 + {9 – {2 × (5 – 2) + 1}} =23

14) 30 – {20 – {5 × (3 – 1) + 1}} 
Solution: 30 – {20 – {5 × (3 – 1) + 1}} = 30 – {20 – {5 × 2 + 1}}
= 30 – {20 – {10 + 1}}
= 30 – {20 – 11}
= 30-9
= 21
Therefore 30 – {20 – {5 × (3 – 1) + 1}} =21

15) 50 + {10 – {6 × (5 – 2) – 1}} 
Solution: 50 + {10 – {6 × (5 – 2) – 1}} =50 + {10 – {6 × 3 – 1}}
=50 + {10 – {18-1}}
=50 + {10-17}
= 50-7
= 43
Therefore 50 + {10 – {6 × (5 – 2) – 1}}   = 43.

16) 72 – {15 + {4 × (3 – 2) + 2}} 
Solution: 72 – {15 + {4 × (3 – 2) + 2}}  = 72 – {15 + {4 × 1 + 2}}
=72 – {15 + {4+2}}
= 72-{15+6}
=72-21
= 51
Therefore  72 – {15 + {4 × (3 – 2) + 2}}  =51

17)40 + {5 – {2 × (5 – 3) + 1}} 
Solution: 40 + {5 – {2 × (5 – 3) + 1}}  =40 + {5 – {2 × 2 + 1}}
= 40 + {5 – {4 + 1}}
=40 + {5 – 5}
= 40
Therefore 40 + {5 – {2 × (5 – 3) + 1}}  = 40.

18) 60 – {16 + {2 × (7 – 2)}} 
Solution: 60 – {16 + {2 × (7 – 2)}}  =60 – {16 + {2 × 5}}
=60 – {16 + 10}
=60- 26
= 34
Therefore 60 – {16 + {2 × (7 – 2)}}  = 34.

19) 21 + 5 × 6 ÷ 3 – 4 
Solution: 21 + 5 × 6 ÷ 3 – 4 =21 + 5 × 2 – 4
=21 + 10 – 4
=31-4
= 27
Therefor 21 + 5 × 6 ÷ 3 – 4 =  27

20) 12 – 3 × 2 + 6 ÷ 2 + 5 
Solution:12 – 3 × 2 + 6 ÷ 2 + 5 =12 – 3 × 2 + 3+ 5
=12 – 6 + 3 + 5
= 20-6
= 14
Therefore 12 – 3 × 2 + 6 ÷ 2 + 5 = 14

21)  48 ÷ 4 + 7 × 3 – 5 
Solution: 48 ÷ 4 + 7 × 3 – 5  =  12 + 7 × 3 – 5
=12 + 21 – 5
=33-5
= 28
Therefore 48 ÷ 4 + 7 × 3 – 5  = 28

22)16 – 4 × 3 + 12 ÷ 6 + 7 
Solution: 16 – 4 × 3 + 12 ÷ 6 + 7  =16 – 4 × 3 + 2 + 7
=16 – 12 + 2 + 7
=25 -12
= 13
Therefore 16 – 4 × 3 + 12 ÷ 6 + 7  =13

23) 10 + 8 ÷ 2 × 5 – 6 
Solution: 10 + 8 ÷ 2 × 5 – 6 =10 + 4 × 5 – 6
=10 + 20 – 6
=30-6
= 24
Therefore 10 + 8 ÷ 2 × 5 -6= 24

24) 30 ÷ 3 + 4 × 5 – 6 
Solution: 30 ÷ 3 + 4 × 5 – 6 =30 ÷ 3 + 4 × 5 – 6
=10+ 4 x 5 -6
=10 + 20 – 6
=30-6
= 24
Therefore 30 ÷ 3 + 4 × 5 – 6 = 24

25) 24 – 6 × 2 + 12 ÷ 4 + 5 
Solution: 24 – 6 × 2 + 12 ÷ 4 + 5 =24 – 6 × 2 + 3 + 5
=24 – 12 + 3 + 5
= 32-12
= 20
Therefore 24 – 6 × 2 + 12 ÷ 4 + 5 = 20

26) 42 ÷ 6 – 3 × 7 + 10 
Solution: 42 ÷ 6 – 3 × 7 + 10 =7 – 3 × 7 + 10
=7 – 21 + 10
=17-21
= -4
Therefore 42 ÷ 6 – 3 × 7 + 10  = -4

27) 60 – 12 ÷ 4 × 5 + 3 
Solution: 60 – 12 ÷ 4 × 5 + 3 =60 – 3 × 5 + 3     (solving division)
=60-15+3              (solving multiplication)
= 63-15                    (solving addition)
= 48
Therefore  60 – 12 ÷ 4 × 5 + 3 = 48

28) 25 + 4 × 7 – 18 ÷ 2 
Solution: 25 + 4 × 7 – 18 ÷ 2  =25 + 4 × 7 – 9               (solving division)
=25+28-9                         (solving multiplication)
= 53-9                                (solving addition)
= 44                                     (solving subtraction)
Therefore  25 + 4 × 7 – 18 ÷ 2  = 44

29) (10 – 2 x 3) ÷ (2 + 1)
Solution:  (10 – 2 x 3) ÷ (2 + 1)  = (10 – 6) ÷  3
= 4 ÷  3
= 1.33

Therefore (10 – 2 x 3) ÷ (2 + 1)  = 1.33

30) 5 + 2 x (7 – 3) ÷ 2 
Solution:  5 + 2 x (7 – 3) ÷ 2  =    5 + 2 x 4 ÷ 2
=  5 + 2 x 2
=5+4
=9
Therefore 5 + 2 x (7 – 3) ÷ 2  = 9

31)  (3 × 4 + 6) ÷ 3 – 2 × 5
Solution: (3 × 4 + 6) ÷ 3 – 2 × 5  =(12 + 6) ÷ 3 – 2 × 5
= 18 ÷ 3 – 2 × 5
=6 -2 x 5
= 6-10
=-4

32 )  -25+14 \div (5-3)
Solution :  -25+14 \div

(5-3)  =-25+14 \div 2
=-25+7
= -18
Therefore -25+14 \div
(5-3)  = -18

33 ) 7 – [6 – {5 – (4 – 3)}] ÷ 2
Solution: 7 – [6 – {5 – (4 – 3)}] ÷ 2 = 7 – [6 – {5 – 1}] ÷ 2
= 7 – [6 – 4] ÷ 2
= 7 – 2 ÷ 2
= 7-1
=6
Therefore 7 – [6 – {5 – (4 – 3)}] ÷ 2 = 6

34) 18 – [6 – {4 – (8 – 6 + 3 )}]
Solution : 18 – [6 – {4 – (8 – 6 + 3 )}] =18 – [6 – {4 – 5}]
=18 – [6 – (-1)]
= 18 – [6+1]
=18- 7
=11

35 ) (45 × 20÷10 + 21) ÷ 3
Solution:
(45 × 20÷10 + 21) ÷ 3  =(45 × 2 + 21) ÷ 3
= (90 + 21) ÷ 3
= 111  ÷ 3
= 37
Therefore (45 × 20÷10 + 21) ÷ 3 =37

36) 5 × (2 + 3) – 7 ÷ 1
Solution: 
5 × (2 + 3) – 7 ÷ 1 =  5 × 5 – 7 ÷ 1
= 5 x 5 -7
=25-7
=18
Therefore 5 × (2 + 3) – 7 ÷ 1 =18

37) \left [ 24\div \left \{ 10-(8-\overline{6-2})\right \} \right ]

Solution : \left [ 24\div \left \{ 10-(8-\overline{6-2})\right \} \right ]

=\left [ 24\div \left \{ 10-(8-4)\right \} \right ]
= [24\div \left \{ 10-4 \right \}]

=24\div 6
                                                                           =4

38)  \mathbf{100\times 10 -100 +2000\div 100}


Solution : 100\times 10 -100 +2000\div 100 = 100\times 10 -100 +20

                                                                                    = 1000-100+20
= 1020-100
=920

Simplify questions for class 6 (unsolved with answers)

Simplify each of the following: 

(i)(3 x 2) -(8-5)

(ii) 30÷ 6+10-2× 5

(iii) (18+10)-(3 x 6)

(iv) 48÷16×2+17-9

(v) (10×8) ÷(20÷5)

(vi) {20+(15+5)}-5

(vii) 121÷ 11+29-2 ×10

(viii) 36 – [18 – {14 – (15 – 4 ÷ 2 x 2)}]

(ix)  45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

(x) 60-48÷6×4+8

(xi) 39-15+18×9÷3

(xii) [29 – (-2) {6 – (7 – 3)}] ÷ [3 x {5 + (-3) x (-2)}]

(xiii) 100-72÷8+4×3

(xiv) 30+75÷15×4-18

(xv) 12-[20÷{8-2(9-5-2)}]

(xvi)  4+4+4+4÷4

(xvii)     25− [4 + {16 − (12 − 2)}]

(xviii)  36 − [18 − {14 − (15 − 4 ÷2 ×2)}]

(xix)  10×10+[400÷{100-(50-)}]

(xx)  [40÷{19-3(6- \overline{4-1})}]

Ans. (i) 2       (ii) 5    (iii) 10    (iv) 14    (v) 20  (vi)  35   (vii) 20  (viii) 21     (ix) 26    (x) 36   (xi) 78   (xii) 1

(xiii)   103      (xiv) 32       (xv)   7    (xvi) 13    (xvii) 15      (xviii) 21     (xix) 105     (xx) 4

Simplification questions for class 6 worksheet PDF

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Simplification  questions quizzes for grade 6

116
Created on

Simplification class 6

1 / 10

 Simplify

(i)   36 - [18 - {14 - (15 – 4 ÷ 2 x 2)}]

2 / 10

(ii)  25− [4 + {16 − (12 − 2)}]

3 / 10

(iii)  12-[20÷{8-2(9-5-2)}]

4 / 10

(iv)  45 - [38 - {60 ÷ 3 – (6 - 9 ÷ 3) ÷ 3}]

5 / 10

(v)  10x10+[400÷{100-(50-\overline{3\times 10})}]

6 / 10

(vi)  [40÷{19-3(6- \overline{4-1}

)}]

7 / 10

(vii) 80+800÷8

8 / 10

(viii) 100\times 10-100+2000÷100

9 / 10

(ix) 6+6-6÷6 x 6

10 / 10

(x) 16 +8 ÷ 4-2 x  3

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