# 30MSC 2023 #23: Think of a Number

In the foreword to our book “Algebra Made Easy as Arithmetic”, Kenneth Williams, the foremost authority in Vedic Math today, wrote:

“It is good to see the appearance of this book as it shows how the simple processes we all learn in Arithmetic have a natural counterpart in Algebra. In addition, the easy and unified Vedic methods make the transition seem almost obvious.

“Algebra is generalized Arithmetic, and the mental process of generalization is one we all unconsciously perform all the time. So, there is nothing really new here, it is a matter of applying out normal thinking in the realm of number…”

Ken Williams introduced the “Think of a Number” technique as a tool for those students who are transitioning from Arithmetic to Algebra.

In our featured example, which was asked in the intermediate level of IVMO 2021, “Which of the following is a possible solution to the equation, x + 1/x = 26/5 ?”, a beginning Algebra student may not be sure how to handle an expression like “ x + 1/x”. But what if he thinks of a number which when its reciprocal is added to it, will give the result 26/5? The denominator 5, immediately suggests that the value of x is 5.

To check, 5 = 25/5 and 25/5 + 1/5 = 26/5.

More examples of mentally solving linear equations are presented in Chapter 3 of our forthcoming book, 30 Master Strategies in Computing Vol III.