BASIC CALCULATION

BASIC CALCULATION:

=>Method 1: square of a number whose unit digit is ‘5’

Let number is “a5” then (a5)²  = (a)*(a+1)  25

i.e. (65)² = (6)*(6+1) 25 =42 25

same as above (125)² = 156 25

=>Method 2: square of a number whose unit digit is ‘1’

Let number is “a1” then (a1)²  =( a²+r)  (2a)  1  {where r is carry over of 2a}

i.e. (51)² = (25+1) (0) 1 =26 0 1 {carry over is 1, comes from 2a= 2*5=10}

same as above (71)² = 50 4 1 and (121)² = 146 4 1

=>Method 3: square of a number whose all digit are ‘1’

(111)² = 12 3 21 , here no of ‘1’= 3

(11111)² = 1234 5 4321 , here no of ‘1’= 5

=>Method 4: square of a normal number

Example 1: (984)² … here it is near 1000 so we are taking base=1000

Now 984 is less than ‘16’ from its base {1000-984=16} so it is represent as “-16”

So (984)² = (984-16)  (16)² here second part should have only 3 digits coz base is 1000

Now (984)²= 968 256 , if in case second part have more than 3 digits, carry over will be added to first part for example: (965)² = (965-35) (35)² = (930) 1225 = (930+1) 225= 931225

Example 2: (93)² … here it is near 100 so we are taking base=100

Now 93 is less than ‘7’ from its base {100-93=7} so it is represent as “-7”

So (93)² = (93-7)  (7)² here second part should have only 2 digits coz base is 100

Now (93)²= 86 49 , if in case second part have more than 2 digits, carry over will be added to first part for example: (86)² = (86-14) (14)² = (72) 1 96 = (72+1) 96= 7396

Example 3: (1012)² … here it is near 1000 so we are taking base=1000

Now 1012 is greater than ‘12’ from its base {1012-1000=12} so it is represent as “+12”

So (1012)² = (1012+12)  (12)² here second part should have only 3 digits coz base is 1000

Now (1012)²= 1024 144 , if in case second part have more than 3 digits, carry over will be added to first part. for example: (1034)² = (1034+34) (34)² = (1064) 1 156 = (1064+1) 156= 1065156

Example 4: (103)² … here it is near 100 so we are taking base=100

Now 103 is greater than ‘3’ from its base {103-100=3} so it is represent as “+3”

So (103)² = (103+3)  (3)² here second part should have only 2 digits coz base is 100

Now (103)²= 106 09 , if in case second part have more than 2 digits, carry over will be added to first part. for example: (112)² = (112+12) (12)² = (124) 1 44 = (124+1) 44= 12544

=>Method 4: multiplication of two numbers if one number is having all the digits as ‘9’

Case 1: A*B (if B>A) then = (A-1)  {B-(A-1)}

45234 * 99999 =  (45234-1) (99999-45233) = 45233 54766

45524*999999 = (45524-1) (999999-45523) = 45523 954476

Case 2: A*B (if B<A) then = (A-1-r)  {B-(A-1)} , here ‘r’ is carry over comes from extra digits ‘A’

2341267 * 99999 = (2341267-1-23) {99999-(2341267-1)} = 2341289 58733

In above example 23 is extra digits from 2341267 so here r=23

74562*9999 = (74562-1-7) {9999-(74562-1)= 74554 5438

In above example 7 is extra digit from 74562 so here r=7

=>Method 5: multiplication of two numbers having same base value

Case 1: 987 X 989 here base=1000 so:   A=987, a =-13 & B=989, b=-11

So 987 X 989= (A-b+r)  (axb)  , second part should be of 3 digits only coz base is 1000, r=0

= 976 143

Ex- 953 X 968 = 921 (1) 504 = 922 504 here r=1

Case 2: 1007 X 1009 here base=1000 so:   A=1007, a =+7 & B=1009, b=+9

Same as above, (1007+9) (7*9)= 1016 063

1071 X 1021= 1092 (1) 491 = 1093 491

Case 3: 1007 X 96 here base=1000 so:   A=1007, a =+7 & B=996, b=-4

In this case some changes in rule, A x B = (A-b-1) (1000-ab)

So, 1007 X 996 = (1007-4-1) (1000-28) = 1002 972

1071 X 951= (1071-49-4) (4000-3479) = 1018 521

## apart from that please learn square of 1 to 25 & cube of 1to 20. Next topic will cover percentage, ratio etc... keep reading. Waiting for ur comments.

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