Easy trick to find multiplication nearest 100,200,300..900
Lets try it with few examples below.
Examples with Base 100
1) Consider two numbers above 100, like 102 and 107.
i. 102 is 2 more than 100 and 107 is 7 more then 100.
ii. Multiply these two numbers ie 2*7=14 to get the ending digits of the final result
iii. Add 102 with 7 or 107 with 2, both giving the same result that’s 109. This make the beginning digits of our final result.
iv. Thus the final result will be 10914 from steps 2 and 3.
2) Consider two numbers below 100, like 97 and 94
i. 97 is 3 less than 100 and 94 is 6 less then 100.
ii. Since the numbers are less than 100 consider minus sign and multiply these two numbers ie -3*-6=18 to get the ending digits of the final result
iii. Add 97 with -6 or 94 with -3, both giving the same result that’s 91. This make the beginning digits of our final result.
iv. Thus the final result will be 9118 from steps 2 and 3.
3) Consider two numbers, one above 100 and other below 100, like 105 and 96.
i. 105 is 5 more than 100 and 96 is 4 less than 100.
ii. Multiply these two numbers ie 5*-4=-20. Keep the value -20 aside.
iii. Add 105 with -4 or 96 with 5 , both giving the same result that’s 101.This make the beginning digits of our final result.
iv. Since our base is 100 put two zeros after the digits got from step 3 that’s 10100.
v. Add digits from step 4 and step 2 that’s 10100+(-20)=10080 to get the final result.
Examples with Base 300
1) Consider two numbers above 300, like 302 and 307.
i. 302 is 2 more than 300 and 307 is 7 more then 300.
ii. Multiply these two numbers ie 2*7=14 to get the ending digits of the final result
iii. Add 302 with 7 or 307 with 2, both giving the same result that’s 109.
iv. Now multiply this with 3 since the base is 300 (if the base was 400 multiply 4 like wise) 109*3=927.This make the beginning digits of our final result.
v. Thus the final result will be 92714 from steps 2 and 4.
2) Consider two numbers below 300, like 297 and 294
i. 297 is 3 less than 100 and 294 is 6 less then 100.
ii. Since the numbers are less than 300 consider minus sign and multiply these two numbers ie -3*-6=18 to get the ending digits of the final result
iii. Add 297 with -6 or 294 with -3, both giving the same result that’s 291.
iv. Now multiply this with 3 since the base is 300 291*3=873.This make the beginning digits of our final result.
v. Thus the final result will be 87318 from steps 2 and 4.
3) Consider two numbers, one above 300 and other below 300, like 305 and 296.
i. 305 is 5 more than 300 and 296 is 4 less than 300.
ii. Multiply these two numbers ie 5*-4=-20. Keep the value -20 aside.
iii. Add 305 with -4 or 296 with 5 , both giving the same result that’s 301.
iv. Now multiply this with 3 since the base is 300 301*3=903.
v. Since our base is 300 put two zeros after the digits got from step 4 that’s 90300.
vi. Add digits from step 5 and step 2 that’s 90300+(-20)=90280 to get the final result.
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