[Algebra] The Escalator Trick -- Part 1

In this article, I introduce an algebraic short-cut. This is for Secondary 1 mathematics in Singapore, approximately grade 7. Let us look at an example.

The standard way is to multiply the left-hand side and the right-hand side by the same number (3, in this case). On the LHS, the threes cancel. The RHS simplifies to 5/2 or 2-and-a-half.

If you notice the effect of multiplying through by 3, it is as if the number 3 has travelled from the lower left side to the upper right side. It is going diagonally across, like one of those escalators you see at shopping malls. So 3 joins the numerator, where you can cancel and simplify. Please make sure you understand the standard way before using the escalator trick.

Here is another example.

The 8 travels up the escalator to the top left. Resist the urge to merge 8×15 into 120. Although this is not wrong, it is inefficient. You get bigger numbers and it is easier to make careless mistakes with bigger numbers. It is much better to try to cancel as much as possible and then simplify. We are left with 3×4 i.e. 12 on the left hand side. That means 12 = x. Applying the Law of Symmetry (if A=B, then B=A), we get x = 12.

Hope you find this useful. Wait for Part 2, which is even more powerful.