Subtraction

In this page we show some method of subtraction that save your time in exam

i) Borrowing and Paying Back Method 

It is faster method of subtraction, we also known as equal addition Method .

Example :

92 - 55 = 37 ,                97-60 = 37

428-179=249,            449-200=249

2826- 1875=951,   2951-2000=951

ii) Double Column Method of Addition And Subtraction

Example   

+7165          

- 1354            

+7834       

- 4321

+1432

---------

11556

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Explain 

step 1    take first double column 32-21=11, 11+34=45, 45-54= -9, -9+65=56

step 2    take second double column 14-43= -29, -29+78 = 49, 49- 13 = 36, 36+ 79 = 115

Thus

Answer 11556

iii) Vinculum Method

Example

+ 3725

-  6783

+ 2502

-  8712

+ 1226

-  8713

-----------

-16755

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Explain

step 1  take first double column 25-83=-58, -58+2=-56, -56-12=-68,  -68+26= -42, -42-13=-55

step 2  take second double column 37-67=-30, -30+25=-5, -5-87=--92, -92+12=-80, -80-57=-167

thus

Answer -16755 

iv) Austrian Method of Subtraction

Example

98765

- 4321

- 2132

- 2212

- 1312

----------

88788

-----------

Explain

step 1)   2+2+2+1 = 7, here 5 is in front of  7, so number greater  than 7 whose unit digit be 5. Let number is 15 . But  7 + 8 = 15  therefore we put at unit place be 8.

Step 2) 1+1+1+3+2= 8, here 6 is front of 8, so number greater than 8 whose unit digit be 6 . Let number be 16 . But 8+8=16 therefore we put at tenth place be 8.

Step 3) 1+3+2+1+3=10, here 7 is in front of 10, so number greater than 10 whose unit digit 7. Let number be 17. But 10+7=17 therefore we put at hundredth place be 7 .

Step 4) 1+1+2+2+4=10, here 8 is in front of 10, so number greater than 10 whose unit digit 8. Let number be 18 . But 10+8=18 therefore we put at thousandth place be 8.

Step 5) 1+9 = 8 we write at ten thousandth place . 1+0 =1, 9 is above of 1 .that 1+8=9 therefore we write 8.

Thus answer is 88788.

v) Digit interchange Method

In this Method we interchange two digit number , add them then sum is equal to sum of digit multiply by 11 .

Example 

     13 + 31 = 44 

(1+3 )X 11 = 44

2)Example

    15 + 51 = 66

(1+5)X 11 = 66

vi) Digit interchange Method for Subtraction

In this Method we interchange two disit number , Subtract them then result is equal to disit multiply by 9.

Example

    62 -26 = 36 

(6-2)X 9 = 36

vii) If Addition and subtraction of consecutive n Natural number then final sum will be -n/2 ,where n is even .

Example

1-2+3-4+5-6+7-8 = ?

Sum = -8/2 = 4

vii) If Addition and subtraction of consecutive n Natural number then final sum will be (n+1)/2 , where n is odd .

Example

1-2+3-4+5-6+7-8+9 = ?

Sum = (9+1)/2 = 5

Exercise

1. 9999 - 888 - 999 - 999 = ?

a) 7113    b) 7112    c) 7733    d) 7142

2. 1-2+3-4+5-6 = ?

a)-3    b) 3    c) -2    d) 2

3. 1-2+3-4+5-6+7 = ?

a) 3    b) 4    c) 2    d) 1

4. 97653-272-2735 = ?

a)94651    b)95641    c)95541    d)99441

5. 3842 +? = 7980 -2089

a)5897    b)2055    c)2165    d) 4055

Answer

1. a    2. a    3. b    4. a    5. b