How to solve 1+(-2)+3(-4)-(-8)=? 

To solve this type of simplification  problem we use ‘BODMAS’ rule. Before applying BODMAS  in the simplification problem which contains brackets follow the steps given below to remove brackets :

Step1:  Solve the inner most bracket first.

Step2 : If a bracket is preceded by a plus sign, remove it by writing its terms as they are.

Step 3: If a bracket is preceded by a minus sign, change positive signs into negative and negative signs into positive with in it. 

Step 4: If there is no sign between a number and a grouping symbol, then it means multiply the number inside the brackets with the number outside the brackets. 

Also we will use the rule how we add Integers that are given below :

1. You add when you have  positive integers .   e.g.  +2+3 =5 , +5+7+8 =20 etc.
2. You also add when you have  negative  integers but the answer will take a ‘-‘ sign . e.g. -2-3=-5 , -5-4-6= -15 etc.
3. When you have one +ve integer and one – ve integer , you must subtract, but answer will take the sign of bigger number. e.g.  -3+7 = +4 ,  -7+4 =-3 etc.

1+(-2)+3(-4)-(-8)=? 

Solution  :  1+(-2)+3(-4)-(-8)= 1-2 – 12  +8    (on multiplying 3 and -4 )
                                                       =  9-2-12            (adding 1 and 8)
= 9-14
=-5

Ans :1+(-2)+3(-4)-(-8)=-5

Easy questions similar to 1+(-2)+3(-4)-(-8) =? 

 1) 5 – 7 – 3 × 2 – (-4) 
Solution:  5 – 7 – 3 × 2 – (-4) = 5 – 7 – 6 + 4                 (Solving multiplication)
= 9-7-6                           ( Adding  4 and 5 )
= 9-13
=-4
Therefore 5 – 7 – 3 × 2 – (-4)   = -4.

2) 2 × 3 – 7 + 5(-2) + 9 
Solution: 2 × 3 – 7 + 5(-2) + 9= 6 – 7 – 10 + 9  [multiplying 2 x 3 and  5  x( -2) ]
=15 -7-10                (adding 6 and 9 )
=15-17
                                               = -2
Therefore 2 × 3 – 7 + 5(-2) + 9 = -2.

3 ) 12 ÷ 4 + 2(-1) – 8 × 0 
Solution: 12 ÷ 4 + 2(-1) – 8 × 0 =  3 +2(-1) -8               (Solving division )
                                                   = 3 – 2 – 0                    (multiplying 2 x (-1))   
                                                   = 1
Therefore   12 ÷ 4 + 2(-1) – 8 × 0 = 1.

4) 5 – 2 × 4 + 3(-1) + 6 
Solution: 5 – 2 × 4 + 3(-1) + 6 =   5 – 8 – 3 +6                 (multiplying 2 x 4 and  3 x -1)
                                                 = 11 – 8 – 3                       (adding  6 and 5)
=11 -11
                                                 = 0
Therefore 5 – 2 × 4 + 3(-1) + 6  = 0.

5) 6 × 2 + 3 – 5(-2) + 1 
Solution: 6 × 2 + 3 – 5(-2) + 1 = 12 + 3 + 10 + 1      (multiplying 6 x 2 and  5 x -2)
                                                = 26
Therefore 6 × 2 + 3 – 5(-2) + 1 = 26.

6) 10 – 3 × 2 + 4(-1) + 6 
Solution: 10 – 3 × 2 + 4(-1) + 6 =   10 -6 -4+6         (multiplying   3 x2 and  4 x (-1) )
= 16-6-4
= 16-10           
                                                   = 6
Therefore 10 – 3 × 2 + 4(-1) + 6  = 6.

7) 15 ÷ 3 – 5 × 2 + 4 
Solution: 15 ÷ 3 – 5 × 2 + 4  = 5- 5 x 2 +4             (performing division)
=5 – 10 + 4               (solving multiplication)
= 9-10                       (performing addition)
= -1                                     (On subtracting)
Therefore 15 ÷ 3 – 5 × 2 + 4  = -1.

8) 7 – 2 × 3 + 5(-1) + 9   
Solution: 7 – 2 × 3 + 5(-1) + 9= 7 – 6 – 5 + 9
= 16-6-5
= 16-11
=5
Therefore  7 – 2 × 3 + 5(-1) + 9= 5.

9) 20 ÷ 4 + 6 – 5(-2) 
Solution:  20 ÷ 4 + 6 – 5(-2)  = 5 +6 -5(-2)
                                              =5 + 6 + 10
                                              = 21
Therefore  20 ÷ 4 + 6 – 5(-2) = 21.

10) 8 – 2 × 4 + 3(-2) + 7 
Solution: 8 – 2 × 4 + 3(-2) + 7 = 8-8 -6+7
                                                 =15 – 8 – 6
=15- 14
                                                 = 1
Therefore 8 – 2 × 4 + 3(-2) + 7 = 1.

11)  30 ÷ 5 + 4 – 3(-1) + 5 
Solution: 30 ÷ 5 + 4 – 3(-1) + 5  = 6 + 4 – 3(-1) + 5 
                                                    =6 + 4 + 3 + 5
                                                    = 18
Therefore 30 ÷ 5 + 4 – 3(-1) + 5  = 18.

12) 12 – 2 × 5 + 3(-3) + 6 
Solution: 12 – 2 × 5 + 3(-3) + 6 =12 – 10 – 9 + 6
                                                  =  18-10-9
= 18-19
=-1.

13 ) 18 ÷ 3 + 6 – 5(-1) + 4
Solution: 18 ÷ 3 + 6 – 5(-1) + 4 =6 + 6 -5(-1) + 4
=6+6 +5+4
                                                   = 21
Therefore 18 ÷ 3 + 6 – 5(-1) + 4 =21.

14 ) 25 – 2 × 6 + 4(-2) + 7 
Solution: 25 – 2 × 6 + 4(-2) + 7 = 25 – 12 – 8 + 7
= 32-12-8
=32-20
                                                 = 12
Therefore 25 – 2 × 6 + 4(-2) + 7  = 12.

15 ) 16 ÷ 4 + 7 – 5(-1) + 3  
Solution: 16 ÷ 4 + 7 – 5(-1) + 3 = 4 +7 -5(-1) +3
                                                  =4 + 7 + 5 + 3
                                                   = 19
Therefore16 ÷ 4 + 7 – 5(-1) + 3 = 19.

Tough questions similar to 1+(-2)+3(-4)-(-8) =? 

1) -2+(-3)-(-4)+(-5)+6  =?
Solution: Since there is + sign before(-3) and (-5) , we will write them as they are and – sign before (-4) , so we change sign of -4 i.e. we will write +4 while removing the bracket.
Hence  -2+(-3)-(-4)+(-5)+6  =  -2-3+4-5+6
= -2-3+10-5        (adding 4 and 6 )
= -10+10               (since -2-3-5=-10)
=0

2) 3(4-5) – 6(2-3) + 7(8-9) = ? 
Solution: 3(4-5) – 6(2-3) + 7(8-9) = 3(-1) – 6(-1) + 7(-1)   (Solving expressions inside small brackets)
=-3 + 6 – 7
=6-10                (-3-7=-10)
=-4

 3) (2-3) + 4(5-6) – 7(8-9) = ?
Solution:  (2-3) + 4(5-6) – 7(8-9) = -1 + 4(-1) – 7(-1)
=-1 – 4 + 7
=-5+7
=2

 4) -5(2-3) + 6(4-5) – 7(8-9) = ?
Solution: -5(2-3) + 6(4-5) – 7(8-9) = -5(-1) + 6(-1) – 7(-1)
=5 – 6 + 7
=12-6
=6

5) -6 – 7(8-9) – 3(4-5) – 2(-3) = ?
Solution:  -6 – 7(8-9) – 3(4-5) – 2(-3) = -6 – 7(-1) – 3(-1) + 6      (Solving expressions inside small brackets)
=-6 + 7 + 3 + 6
=-6+16
=10

6) 2(3+4) – 5(6-7) + 8(9-10) = ?
Solution:  2(3+4) – 5(6-7) + 8(9-10) =2(7) – 5(-1) + 8(-1)
=14 + 5 – 8
=19-8
=11

7) -3(4-5) – 6(2-3) – 7(8-9) = ?
Solution: -3(4-5) – 6(2-3) – 7(8-9) = -3(-1) – 6(-1) – 7(-1)
=3 + 6 + 7
= 16

8) 4(-5+6) + 3(2-3) – 8(7-9) = ?
Solution:     4(-5+6) + 3(2-3) – 8(7-9) = 4(1) + 3(-1) – 8(-2)
= 4 – 3 + 16
= 20-3
=17

9) -2+(-3)-(-4)+(-5)+6 = ?
Solution:  -2+(-3)-(-4)+(-5)+6 = -2 + (-3) + 4 + (-5) + 6
= -2-3+4-5+6
= -10+10
=0

10) 3(4-5) – 6(2-3) + 7(8-9) = ?
Solution: 3(4-5) – 6(2-3) + 7(8-9) =3(-1) – 6(-1) + 7(-1)
= -3 + 6 – 7
=-10+6
= -4

11) (2-3) + 4(5-6) – 7(8-9) = ?
Solution: (2-3) + 4(5-6) – 7(8-9) =  -1 + 4(-1) – 7(-1)
= -1 – 4 + 7
=-5+7
= 2

12 ) -5(2-3) + 6(4-5) – 7(8-9) = ?
Solution: -5(2-3) + 6(4-5) – 7(8-9) = -5(-1) + 6(-1) – 7(-1)
= 5 – 6 + 7
=12-6
= 6

13 ) -6 – 7(8-9) – 3(4-5) – 2(-3) = ?
Solution: -6 – 7(8-9) – 3(4-5) – 2(-3) = -6 – 7(-1) – 3(-1) – 2(-3)
= -6 + 7 + 3 +6
=-6+16
=10

14) 2(3+4) – 5(6-7) + 8(9-10) = ?
Solution: 2(3+4) – 5(6-7) + 8(9-10) =  2(7) – 5(-1) + 8(-1)
= 14 + 5 – 8
=19-8
= 11

15 ) -3(4-5) – 6(2-3) – 7(8-9) = ?
Solution: -3(4-5) – 6(2-3) – 7(8-9) =-3(-1) – 6(-1) – 7(-1)
= 3 + 6 + 7
= 16

16) 4(-5+6) + 3(2-3) – 8(7-9) = ?
Solution: 4(-5+6) + 3(2-3) – 8(7-9) = 4(1) + 3(-1) – 8(-2)
= 4 – 3 + 16
=20-3
= 17

17) 3(-4+5) – 6(8-7) – 2(-9) = ?
Solution: 3(-4+5) – 6(8-7) – 2(-9) =  3(1) – 6(-1) – 2(-9)
= 3 + 6 + 18
= 27

18) 2(-3+4) + 5(6-5) – 8(10-9) = ?
Solution: 2(-3+4) + 5(6-5) – 8(10-9) = 2(1) + 5(1) – 8(1)
= 2 + 5 – 8
=7-8
= -1

19 ) -4(3-2) – 5(8-7) – 6(-9+10) = ?
Solution: -4(3-2) – 5(8-7) – 6(-9+10) = -4(1) – 5(1) – 6(1)
= -4 – 5 – 6
= -15

20) 5(-2+3) + 6(-4+5) + 7(9-10) = ?
Solution: 5(-2+3) + 6(-4+5) + 7(9-10) = 5(1) + 6(1) + 7(-1)
= 5 + 6 – 7
= 11-7
= 4

21) 3(7-5)+4(6-3)+5(4-2) = ?
Solution: 3(7-5)+4(6-3)+5(4-2) = 3(2) + 4(3) + 5(2)
= 6 + 12 + 10
= 28

22) -7(8-4)+6(7-3)-5(6-2) = ?
Solution: -7(8-4)+6(7-3)-5(6-2) = -7(4) + 6(4) – 5(4)
= -28 + 24 – 20
= -48+24
= -24

 23) -6(4-2)+5(6-4)-4(8-6) = ?
Solution: -6(4-2)+5(6-4)-4(8-6) =-6(2) + 5(2) – 4(2)
= -12 + 10 – 8
=-20+10
= -10

24) 5(6-7)-6(5-6)+7(4-5) = ?
Solution: 5(6-7)-6(5-6)+7(4-5) =  5(-1) – 6(-1) + 7(-1)
= -5 + 6 – 7
= -12+6
= -6

25) -3(4-6)+4(6-4)-5(2-4) = ?
Solution: -3(4-6)+4(6-4)-5(2-4) = -3(-2) + 4(2) – 5(-2)
                                                               = 6 + 8 + 10
                                                               = 24

26) 5(3-5)-6(2-4)-7(1-3) = ?
Solution: 5(3-5)-6(2-4)-7(1-3) = 5(-2) – 6(-2) – 7(-2)
                                                            = -10 + 12 + 14
                                                             =-10 +26
                                                            = 16

27)  6(2-4)-7(1-3)+8(0-2) = ?
Solution: 6(2-4)-7(1-3)+8(0-2) = 6(-2) – 7(-2) + 8(-2)
                                                              = -12 + 14 – 16
                                                              =-28+14
                                                              = -14

28) -4(5-7)+5(4-6)-6(3-5) = ?
Solution:  -4(5-7)+5(4-6)-6(3-5) = -4(-2) + 5(-2) – 6(-2)
                                                               = 8 – 10 + 12
                                                               = 20-10
                                                               =10

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Toughest questions similar to 1+(-2)+3(-4)-(-8) with their solutions:

1) 2(3-4)+5(2-3)-3(4-5)+7(9-10)-8(7-9) = ?
Solution: 2(3-4)+5(2-3)-3(4-5)+7(9-10)-8(7-9) = 2(-1)+5(-1)-3(-1)+7(-1)-8(-2)   (Solving expression inside the brackets)
= -2-5+3-7+16
= -14 +19                                    (Since -2-5-7 =-14)
= 5                                                                  

2) -5(6-7)+7(9-10)+4(8-9)+2(3-4)-6(-5+6) = ? 
Solution: -5(6-7)+7(9-10)+4(8-9)+2(3-4)-6(-5+6) = -5(-1)+7(-1)+4(-1)+2(-1)-6(1)
= 5-7-4-2-6
=5-19
                                                                               =  -14

3) 3(-4+5)-5(6-5)+8(10-9)-2(3-4)+6(-5+6) = ?
Solution: 3(-4+5)-5(6-5)+8(10-9)-2(3-4)+6(-5+6) = 3(1)-5(1)+8(1)-2(-1)+6(1)
= 3-5+8+2+6
=19-5
=14

4) -4(-3+4)+5(7-8)-6(9-8)-3(-2)-2(3-4) = ?
Solution: -4(-3+4)+5(7-8)-6(9-8)-3(-2)-2(3-4) = -4(1)+5(-1)-6(1)-3(-2)-2(-1)
= -4-5-6+6+2
=-15 +8
= -7

5) 7(3-4)-4(-5+6)+2(9-10)-5(-2+3)-8(7-9) = ?
Solution: 7(3-4)-4(-5+6)+2(9-10)-5(-2+3)-8(7-9) = 7(-1)-4(1)+2(-1)-5(1)-8(-2)
= -7-4-2-5+16
=-18+16
                                                                               = -2

 6 ) -3(6-7)+4(-2+3)+5(10-9)+6(-5+6)-7(9-10) = ?
Solution: -3(6-7)+4(-2+3)+5(10-9)+6(-5+6)-7(9-10) = -3(-1)+4(1)+5(1)+6(1)-7(-1)
= 3+4+5+6-7
=18-7
= 11

7) 5(-2+3)-6(8-7)-7(-9+10)+3(4-5)-2(-3+4) = ? 
Solution: 5(-2+3)-6(8-7)-7(-9+10)+3(4-5)-2(-3+4) =5(1)-6(1)-7(1)+3(-1)-2(1)
= 5-6-7-3-2
= 5-18
= -13

8) 10 – 2(4) + 3(6) – (-5) =?
Solution:  10 – 2(4) + 3(6) – (-5) =  10 -8 +18+5
= 33- 8
=25

9) $(-1+3-1)\times 2+(-2)-1$

Solution:  $(-1+3-1)\times 2+(-2)-1$

${\displaystyle \mathrm{= \; (-2+3)\; x\; 2+(-2)\; -1\; =(1)\; x\; 2\; +(-2)\; -1\; =\; 2-2-1\; =2-3\; =-1}}$

10) -3-((-1)-2 x2) =?
Solution: –3-((-1)-2 x2) =-3-((-1)-4)
=-3-(-1-4)
=- 3-(-5)
=-3+5
=2

11) 
Solution: 4+6

(-3 x 2)=   4+6(-6)
= 4 +(-1)
=4-1
=3

12) -6(-3+5)+7(-2+4)+4(-9+10)-2(6-8)+5(8-9) = ?            
Solution : -6(-3+5)+7(-2+4)+4(-9+10)-2(6-8)+5(8-9) = -6(2) +7(2) +4(1) -2(-2)+5(-1)
=-12+14+4+4-5
= -17 + 22
=5       

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