NCERT Book Class 8 Mathematics (Part II) Chapter 6 Algebra Play

ALGEBRA PLAY
6

6.1 Algebra Play
Over the last two years, we have used algebra to model different
situations. We have learned how to solve algebraic equations and find
the values of unknown letter-numbers. Let’s now have some fun with
algebra. We shall investigate tricks and puzzles, and explain why they
work using algebra. We will also see how to invent new tricks and
puzzles to entertain others.

6.2 Thinking about ‘Think of a Number’ Tricks
In Grade 7, we learned about ‘Think of a Number’ tricks, like this one.
1. Think of a number.
2. Double it.
3. Add four.
4. Divide by two.
5. Subtract the original number you thought of.

I predict you get 2. Am I right? Try it out with different starting numbers.
Do you always end up with the same value, 2? Why?

We saw that we can understand such tricks through algebra.
1. Think of a number: x
2. Double it: 2x
3. Add four: 2x + 4
4. Divide by 2: x + 2
5. Subtract the original number you thought of: x + 2 – x = 2
Therefore, no matter what the starting number is, the end result will
always be 2!