Multiplication using Reference: Part 2

Multiplication Using reference: Part 2

Kids! This section is added after getting motivation from the Daughter of Shri Dayanand Kumar, a senior scientist is DRDO. This part is an extension to previous post and many similar additional posts will come, as the topic has many diversions.

This post discusses mental multiplication using reference 100. In previous post, either both the multipliers were less than 100 or both were more than 100. In this section, those multiplications will be explained, where, one number is less than reference and other is more than reference.

For 108x98, differences from reference (100) are +8 and -2, respectively. The product has two parts. The left side digit will be 108-2 = 98+8 = 106. The right partition has two digits, given by product of these differences, +8x-2 = -16. This can be written as -16 = 84 -100 = -100+84 = 184. (underline denotes negative term). Now it has three terms, but only 2-digits are specified for right side. So, -1 is carried over to left side and left side digit becomes 106-1 = 105. So, 108x98 = 10584. Some more examples are solved.

108x98 = 108-2|+8x-2 = 106|-16 = 106|84-100 = 106|184 = 106-1|84 = 105|84 = 10584

108x98 = 98+8|+8x-2 = 106|-16 = 106|84-100 = 106|184 = 106-1|84 = 105|84 = 10584

112x97 = 112-3|+12x-3 = 109|-36 = 109|164 = 109-1|64 = 108|64 = 10864

112x97 = 97+12|+12x-3 = 109|-36 = 109|164 = 109-1|64 = 108|64 = 10864

107x88 = 107-12|+7x-12 = 95|-84 = 95|116 = 95-1|16 = 94|16 = 9416

107x88 = 88+7|+7x-12 = 95|-84 = 95|116 = 95-1|16 = 94|16 = 9416

112x88 = 112-12|+12x-12 = 100|-144 = 100|256 + 100-2|56 = 9856

112x88 = 88+12|+12x-12 = 100|-144 = 100|256 = 100-2|56 = 9856

119x83 = 119-17|+19x-17 = 102|-323 = 102|477 = 102-4|77 = 9877

119x83 = 83+19|+19x-17 = 102|-323 = 102|477 = 102-4|77 = 9877

This post is mainly to introduce the concept of negative part in a number in mental mathematics. The concept, if understood can be used with ease for solving the above multiplications in slightly different way also.

108x98 = 108x102 = 108-2|8x-2 = 106|-16 = 106|184 = 106-1|84 = 10584

112x97 = 112 x 103 = 112-3|12x-3 = 109|-36 = 109|164 = 109-1|64 = 108|64 = 10864

107x88 = 107x112 = 107-12|7x-12 = 95|-84 = 95|116 = 95-1|16 = 94|16 = 9416

112x88 = 112x112 = 112-12|+12x-12 = 100|-144 = 100|256 = 100-2|56 = 9856

119x83 = 119x117 = 119-17|+19x-17 = 102|-323 = 102|477 = 102-4|77 = 9877

67x 114 = 133x114 = 114-33|14x-33 = 81|-462 = 81|538 = 81-5|38 = 7638

More of similar examples can be solved and power of mental mathematics can be felt. Hope that introduction of negative part in a number is understood by kids. It needs practice as concept is entirely different from conventional approach. Enjoy it.

Dr Himanshu Shekhar