Chapter 1: The Challenge of Calculator-Free Calculation

Algebra is captivating because it allows us to assess expressions using only our minds. The thrill of math puzzles is in the ability to tackle and comprehend them without relying on technology.

So, the question arises: Can your brain help you find the correct solution?

I encourage you to pause here, take out a pen and paper, and try solving this puzzle on your own. Once you're finished, continue reading for the answer!

Video Description: This video demonstrates simple calculations without the use of a calculator, perfect for Grade 11 students.

As you approach the solution, observe that the numbers involved are consecutive integers. We can designate 2019 as x, transforming the expression into a more manageable form.

Next, we will organize the terms as demonstrated below.

After that, we will expand the brackets in this manner:

Rearranging the quadratic into two bracket expressions yields the following result:

Notice how the terms within the brackets follow a specific format:

In this case, we can define A as the quadratic expression and B as 1. Therefore, we can derive:

From here, we can simplify our result to:

The final sum is as follows:

And there you have it—the answer is revealed!

Isn't it fascinating?

What went through your mind as you worked on this? Feel free to share your thoughts in the comments below; I'm excited to hear from you!

Don’t forget to check out the following video to enhance your skills further.

Video Description: Rob Eastaway shares techniques for performing math calculations without a calculator, designed for all ages.