SHORT CUT TO FIND SQUARES FROM50 TO 60

With out doing actual multiplication another interesting & shortcut method is there to find 50² to 60²

50²= 5²+0,0² =2500(here write 0²=00)

51²= 5²+1 ,1² =2601

52²= 5²+2 ,2²=2704

53²= 5²+3 , 3²=2809

54²= 5²+4 ,4²=2916

55²= 5²+5 ,5² =3025

56²= 5²+6 ,6² = 3136

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FINDING SQUARES FROM 21 TO 30

In the last post you learned how to find squares from 11

11² =11+1 ,1² =121

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To day let us find 21² to 30²

21² = 2X(21+1) ,1² =441

22² = 2X(22+2) ,2² =484

23² = 2X(23+3) ,3² = 529

24² = 2X(24+4) ,4² = 56,16 =576(carry 1 & add it to56)

25² = 2X(25+5) ,5² = 60 ,25 =625 (carry 2 & add it to 60)

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Similarly

31² = 3(31+1) ,1² =961

32² = 3(32+2) ,2² =1024

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SHORTCUT TO FIND SQUARES FROM 11

11² =11X11

without doing actual multiplication we can do it in a simple way.

11² = 11+1, 1² =121

12² =12+2, 2² =144

13² = 13+3, 3² =169

14² = 14+4, 4² =18,16 =196 (carry 1 &add it to18)

15² =15+5, 5² =20,25 =225 (carry 2 & add it to 20)

16² =16+6, 6² =22,36 =256 (carry 3 &add it to 22)

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SHORTCUTS IN MULTIPLICATION

Multiplication of two numbers whose tens digits are same and sum of the unit digits is 10.

example: 97x93
84x86
72x78

Multiply the ten's digit with its next integer and write the product of unit digits next to it
97x93= (9x10),7x3 =9021
84x86= (8x9),4x6 =7224
72x78= (7x8),2x8 =5616
This rule is also applicable for three digit numbers whose sum of unit digits is 10 and the remaining digits are same.
113x117= (11x12),3x7 =13221
128x122= (12x13),8x2=15616
The same rule is applicable to find the squares of numbers whose unit digit end with 5.
square of 15 = 15x15 =1x2,5x5 = 225
square of 25 = 25x25 = 2x3, 5x5 = 625
square of 35 = 35x35 = 3x4, 5x5 = 1225
square of 45 = 45x45 = 4x5, 5x5 = 2025

square of 125 =12x13,5x5=15625

SHORTCUT FOR MULTIPLICATION OF11

SHORTCUT FOR MULTIPLICATION OF11

Consider 11 x 35

Take 35 and separate the digits

Add 3+5. Put the 8 in between 3&5.

We get 385

Therefore 11x35=385

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If the number being multiplied has digits that add up to more then 9, you simply carry over to the first digit. For example:

Consider 11 x 57

Take 57 and separate the number

Add 5&7=12

add 1 to the first digit 5, it gives 6.

and put the 2 in the middle. You end up with 627

Therefore 11x57=627.

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MULTIPLICATION OF NUMBERS CLOSE TO10^3(=1000)

This method is very easy when compared with general multiplication, but useful only when the numbers are close to powers of 10.

Ex 1) 998x987

• here 998 is 2 less than 1000& 987 is 13 less than 1000.
• multiply 2&13. And write it as 026
• now take 998-13 or987-2 which is equal to 985 (cross subtraction)
  

• therefore 998x987=985026

998........2
X 987........13
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985 026
here 985=998-13 or 987-2(cross subtraction)
026=2X13
Therefore 998x987= 985026

Ex:2) 1007x1013

• here 1007 is 7 more than 1000&1013 is 13 more than 1000
• multiply 7&13 and write it as 091
• now take 1007+13 or 1013+7 (cross addition) which is equal to1020.
• therefore 1007x1013=1020091

1007................7
X 1013..............13
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1020 091

Therefore 1007X1013 =1020091

MULTIPLICATION OF NUMBERS CLOSE TO 100

EX :1) 98x97
98 is 2 less than 100& 97 is 3 less than 100.
now multiply 2&3
write 2x3=06
and then take 98-3 or 97-2 which is equal to 95
therefore ans is 9506.

98.............2
x 97...............3
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95 06
here 95= 98-3 or 97-2 (cross subtraction)
06=2x3

so 98x97=9506

ANOTHER EXAMPLE: 108X109
Here 108 is 8 more than 100&109 is 9 more than100
now multiply 8&9
and write it as 72
now take 108+9 or109+8.which is =117
THEREFORE 108x109=11772

108.........8
x 109..........9
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117 72

here 117=108+9 or 109+8
72=8x9

THEREFORE 108X109= 11772

MULTIPLICATION OF NUMBERS CLOSE TO 10

A)MULTIPLICATION OF NUMBERS CLOSE TO 10.

EX: 1 9X8 9 is 1 less than 10& 8 is 2 less than 10. now multiply 1&2
write in this way

9...........1
x8...........2
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7 2 Here 7= 9-2 or 8-1 (cross subtraction)
2=1x2
therefore 9x8=72.

EX:2 12X14 12 is 2 more than 10 &14 is 4 more than 10

12..........2
x 14..........4
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16 8 here 8=2x4 and 16=12+4 or 14+2(cross addition)

there fore 12x14=168