Multiplying two numbers both of which are close to the same power of 10 using Speed Mathematics

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 983042

Multiplying two numbers both of which are close to the same power of 10 using Speed Mathematics