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

*of numerator to denominator, which those ignorant will not be able to comprehend.*

**simple flipping**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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