Example 1
Calculate 98 * 93
Solution
Select a closest base ( a power of 10). In this case we can select 100 as a base. Write these numbers with the difference from the base. That is 98-100 = -2 and 93-100 is -7. So write it as
98 : -2
93 : -7
Left side of the answer will be the diagonal sum including their signs. That is 98-7=91. So 91 will be the left side of the product. (You can take the other diagonal sum also, that is 93-2=91. Always these diagonal sums will be same).
To find the right hand side, just multiply the differences including their signs. That is -2 * -7 = 14
So we got that left side of the product is 91 and right side is 14. So answer is 9114
Example 2
Calculate 96 * 112
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 96-100 = -4 and 112-100 is 12. So write it as
96 : -4
112 : 12
Take the diagonal sum to get the left side of the product. That is 96+12 = 108 (Or 112-4 = 108).
For the right side, find the product of the differences. That is -4*12 = -48. Since it is -ve, we need to make it as +ve. For this borrow 1 from our left hand side 108. This borrowed 1 becomes 100 and our right hand side becomes 100+(-48) = 52. This is our right hand side
Since we borrowed one from left hand side, left hand side is 107
So answer is 10752
Example 3
Calculate 103 * 115
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 103-100 = 3 and 115-100 is 15. So write it as
103 : 3
115 : 15
Take the diagonal sum to get the left side of the product. That is 103+15 = 118 (Or 115+3= 118).
For the right side , find the product of the differences. That is 3*15 = 45.
So answer is 11845
Example 4
Calculate 122 * 89
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 122-100 = 22 and 89-100 is -11. So write it as
122 : 22
89 : -11
Take the diagonal sum to get the left side of the product. That is 122+(-11) = 111 (Or 89+22= 111).
For the right side , find the product of the differences. That is 22*(-11) = -242. Since it is -ve, we need to make it as +ve. For this borrow 3 from our left hand side 111. This borrowed 3 becomes 300 and our right hand side becomes 300+(-242) = 58. This is our right hand side
Since we borrowed 3 from left hand side, left hand side is 108
So answer is 10858
Example 5
Calculate 1024 * 989
Use the same method. Let's select 1000 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 1024-1000 = 24 and 989-1000 is -11. So write it as
1024 : 24
989 : -11
Take the diagonal sum to get the left side of the product. That is 1024+(-11) = 1013 (Or 989+24= 1013).
For the right side, find the product of the differences. That is 24*(-11) = -264. Since it is -ve, we need to make it as +ve. For this borrow 1 from our left hand side 1013. This borrowed 1 becomes 1000 and our right hand side becomes 1000+(-264) = 736.
Since we borrowed 1 from left hand side, left hand side is 1012 now.
So our answer is 1012736
Example 6
Calculate 997 * 986
Use the same method. Let's select 1000 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 997-1000 = -3 and 986-1000 is -14. So write it as
997 : -3
986 : -14
Take the diagonal sum to get the left side of the product. That is 997+(-14) = 983 (Or 986-3= 983).
For the right side, find the product of the differences. That is (-3)*(-14) = 42. But here 42 has only 2 digits whereas our base 1000 has three zeros. So write 42 as 042.
So our answer is 98304
Calculate 98 * 93
Solution
Select a closest base ( a power of 10). In this case we can select 100 as a base. Write these numbers with the difference from the base. That is 98-100 = -2 and 93-100 is -7. So write it as
98 : -2
93 : -7
Left side of the answer will be the diagonal sum including their signs. That is 98-7=91. So 91 will be the left side of the product. (You can take the other diagonal sum also, that is 93-2=91. Always these diagonal sums will be same).
To find the right hand side, just multiply the differences including their signs. That is -2 * -7 = 14
So we got that left side of the product is 91 and right side is 14. So answer is 9114
Example 2
Calculate 96 * 112
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 96-100 = -4 and 112-100 is 12. So write it as
96 : -4
112 : 12
Take the diagonal sum to get the left side of the product. That is 96+12 = 108 (Or 112-4 = 108).
For the right side, find the product of the differences. That is -4*12 = -48. Since it is -ve, we need to make it as +ve. For this borrow 1 from our left hand side 108. This borrowed 1 becomes 100 and our right hand side becomes 100+(-48) = 52. This is our right hand side
Since we borrowed one from left hand side, left hand side is 107
So answer is 10752
Example 3
Calculate 103 * 115
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 103-100 = 3 and 115-100 is 15. So write it as
103 : 3
115 : 15
Take the diagonal sum to get the left side of the product. That is 103+15 = 118 (Or 115+3= 118).
For the right side , find the product of the differences. That is 3*15 = 45.
So answer is 11845
Example 4
Calculate 122 * 89
Solution
Use the same method. Let's select 100 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 122-100 = 22 and 89-100 is -11. So write it as
122 : 22
89 : -11
Take the diagonal sum to get the left side of the product. That is 122+(-11) = 111 (Or 89+22= 111).
For the right side , find the product of the differences. That is 22*(-11) = -242. Since it is -ve, we need to make it as +ve. For this borrow 3 from our left hand side 111. This borrowed 3 becomes 300 and our right hand side becomes 300+(-242) = 58. This is our right hand side
Since we borrowed 3 from left hand side, left hand side is 108
So answer is 10858
Example 5
Calculate 1024 * 989
Use the same method. Let's select 1000 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 1024-1000 = 24 and 989-1000 is -11. So write it as
1024 : 24
989 : -11
Take the diagonal sum to get the left side of the product. That is 1024+(-11) = 1013 (Or 989+24= 1013).
For the right side, find the product of the differences. That is 24*(-11) = -264. Since it is -ve, we need to make it as +ve. For this borrow 1 from our left hand side 1013. This borrowed 1 becomes 1000 and our right hand side becomes 1000+(-264) = 736.
Since we borrowed 1 from left hand side, left hand side is 1012 now.
So our answer is 1012736
Example 6
Calculate 997 * 986
Use the same method. Let's select 1000 as the base (Closed to both of the numbers).Write these numbers with the difference from the base. That is 997-1000 = -3 and 986-1000 is -14. So write it as
997 : -3
986 : -14
Take the diagonal sum to get the left side of the product. That is 997+(-14) = 983 (Or 986-3= 983).
For the right side, find the product of the differences. That is (-3)*(-14) = 42. But here 42 has only 2 digits whereas our base 1000 has three zeros. So write 42 as 042.
So our answer is 98304
