In the section, “Multiplying numbers just above 10“, we discussed how to multiply 2 numbers which are near base 10.
Similar method can be used to multiply 2 numbers which are near base 100. There are 2 parts of the answer, left part (which is most significant part) and right part (which is least significant part). The figures on the right are obtained by finding how much is the number above or below 100. If the number is above 100, then figure is positive and if the number is below 100, then figure is negative. To get right part of the answer, we multiply figures on the right vertically. And to get the left part of the answer, we add the 1st number crosswise with 2nd figure or 2nd number crosswise with 1st figure.
There can be 3 cases:
- Case 1: Multiplying numbers just above 100
Let us understand this method with an example.
102 x 112
102 is 2 above 100
112 is 12 above 100
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically (2 x 12).
To get left part, we perform crosswise addition of 1st number with 2nd figure on right (102 + 12) or 2nd number with 1st figure on right (112 + 2).
- Case 2: Multiplying numbers just below 100
Let us understand this method with an example.
98 x 88
98 is 2 below 100
88 is 12 below 100
The important thing to remember is to keep the ‘-‘ sign along with the figure.
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically (-2) x (-12).
To get left part, we perform crosswise addition of 1st number with 2nd figure on right 98 + (-12) = 86, or 2nd number with 1st figure on right 88 + (-2) = 86.
- Case 3: Multiplying numbers on either side of 100
Let us understand this method with an example.
112 x 98
112 is 12 above 100
98 is 2 below 100
The important thing to remember is to keep the ‘-‘ sign along with the above figures.
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically (12) x (-2) = -24
To get left part, we perform crosswise addition of 1st number with 2nd figure on right 112 + (-2) = 110, or 2nd number with 1st figure on right 98 + (12) = 110.
With this method, we can multiply any pair of numbers which are close to base 100; For example: 112 x 105, 113 x 107, 111 x 104, 102 x 98, 113 x 99, 98 x 86, 91 x 92 etc.
Maths is Fun and Easy 