Simple Flipping of Math Terms

Math equations are interesting. They are more so when used in algebra for checking of understanding.

Many weird answers can come out when done wrongly.

Look at an example of changing numerator to denominator of terms in an equation.

Example: Express y in terms of x for the equation (1 / y) = 5 + x

If the answer is simply to "flip" numerator to denominator,

getting y = (1/5) + (1/x), did the student learn his lesson?

Yes, he applied the concept of x / y = a / c ==> y / x = c / a neatly, but......

something went amiss!

First loophole: Student did not understand the meaning of "="

Second loophole: Student did not understand the meaning of summation

Why?

* Right Concept

First item:
The "=" symbol means whatever collectively on the left equals whatever collectively is on the right side.

Second item:
The "+" symbol means terms are added up to form a bigger piece of "something".
This bigger piece of "something" therefore operates as a whole, and not as individual terms.

The correct answer, hereby, should be, following the above 2 concepts,

(1 / y) = 5 + x ===> y = 1 / (5 + x)

The whole of "5 + x" acts as a collectively bigger piece of "something", and is flipped together as a single piece.

Note, however, here the word "flipped" has many "stories" within it.

Like to hear the "stories"? Read on....

Flipping is an abbreviation for the cross multiplication operation.

Mathematically speaking, it is

1/y = 5 + x ==> Multiply both side by "y"==> (1/y) * y = (5 + x) * y

==> 1 = (5 + x) * y, the "y" is brought over.

Divide both side by "(5 + x)" ==> 1 / (5 + x) = [(5 + x) * y] / (5 + x)

==> 1 / (5 + x) = y .The correct answer.

Finally, at long last, we obtain the outcome of the "flipping".

You can see from the above that if you understand the math principle, you can actually do simple flipping of numerator to denominator, which those ignorant will not be able to comprehend.

They will simply follow the flipping and will get flopped at the end.

Message:
Understand what you are doing. Equations in algebra can reveal your ignorance!

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