[Algebra] Flipping Fractions

Here is a problem done by standard orthodox methods.

Flipping Trick - 01.jpg

We multiply both sides of tbe equation by 3x, which is a legit procedure. On the LHS, we cancel the x's, and on the RHS, we cancel the 3s. We now have 3 = 5x. We need to get rid of the 5, so we divide both sides by 5. After cancelling, we get 3/5 = x. Then by the Law of Symmetry (if A=B, then B=A), we can conclude that x = 3/5.

This takes 4 steps to solve. Is there a faster way? You can try the Escalator Trick
like this:-

Flipping Trick - 02.jpg

Move the x up the escalator to appear on top of the other side. Now 5 and 3 have to move. So 5 moves down the escalator to the bottom left side, and 3 moves up the escalator to the top of the left side. Again by the Law of Symmetry (if A=B, then B=A), we can conclude that x = 3/5.

Not bad. But it takes 2 steps. It there an even faster way?
Yes! Think of two chicken wings on a barbecue skewer. If you flip the skewer, both the chicken wings flip together.

Flipping Trick - 03.jpg

Now we do this flipping for our equation.

Flipping Trick - 04.jpg

We invert (calculate the reciprocal) both the LHS and the RHS at the same time. And we get the answer immediately. The reason this works is because 1 ÷ (1/x) = x and 1 ÷ (5/3) = 3/5, and we are doing the same thing to both sides, so we still get things that are equal. Note that x/1 is the same as x. So we do not need to write the '/1' actually.

There we have it! This short-cut is flipping good, eh?

H2
H3
H4
3 columns
2 columns
1 column
1 Comment