Doing Algebra Mentally

A few days ago, I posted an entry It’s a magnificient time to know math. So I decided to keep an eye out for any resources that teach math or articles that show how to teach math. Today I came across this link in on Inner Algebra. It is the text of a book and looks very interesting.

Whenever I talk to a small group about Thinking and Problem Solving, I always try a few mental math questions. For example, what is 29*31. You can instantly answer this as 899 if you know a simple algebraic equation. Here are the mental steps:

Step-1: 29 * 31 = (30-1)* (30+1)

Step-2: (30-1)*(30+1) = 30*30 – 1*1

This based on the algebraic equation (a+b)*(a-b) = a^2-b^2

Step-3: 900 -1 = 899

You may not encounter these type of problems in every day life. But if you develop a mind set to solve problems mentally, life will be a lot more fun.

When I was in India in August, one of my favoire nephews (he is 11 years old) asked us to solve a simple equation. a^b+b^a= 100. What are the values of a and b? ( “a” to the power of “b” + “b” to the power of “a”).