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Genrish500 [490]
3 years ago
9

What is 1/3 divided by 5/6

Mathematics
2 answers:
Stells [14]3 years ago
8 0
(1/3)/(5/6)=(1/3)/(6/5)=6/15
kykrilka [37]3 years ago
8 0
0.0666 because 1/3 divided by 5/6
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Use complete sentences to describe why √-1 ≠ -√1
tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u>

\displaystyle \large{ {y}^{2}  = x} \\  \displaystyle \large{ y =  \pm  \sqrt{x} }

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>I</u><u>I</u>

\displaystyle \large{  {a}^{2}  = a \times a =  |b| }

Where b is the result from a×a. Let's see an example.

<u>E</u><u>x</u><u>a</u><u>m</u><u>p</u><u>l</u><u>e</u><u>s</u>

\displaystyle \large{  {2}^{2}  = 2 \times 2 = 4} \\  \displaystyle \large{  {( - 2)}^{2}  = ( - 2) \times ( - 2) =  | - 4|  = 4}

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

\displaystyle \large{   {y}^{2}  =  - 1}

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

\displaystyle \large{   \sqrt{ {y}^{2} } =   \sqrt{ - 1}  }

Then where does plus-minus come from? It comes from one of Absolute Value propety.

<u>A</u><u>b</u><u>s</u><u>o</u><u>l</u><u>u</u><u>t</u><u>e</u><u> </u><u>V</u><u>a</u><u>l</u><u>u</u><u>e</u><u> </u><u>P</u><u>r</u><u>o</u><u>p</u><u>e</u><u>r</u><u>t</u><u>y</u><u> </u><u>I</u>

\displaystyle \large{  \sqrt{ {x}^{2}  } =  |x|  }

Solving absolute value always gives the plus-minus. Therefore...

\displaystyle \large{  y =   \pm \sqrt{ - 1}  }

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

\displaystyle \large{   {y}^{2}  = 1} \\  \displaystyle \large{    \sqrt{ {y}^{2} }  =  \sqrt{1} } \\  \displaystyle \large{  y  =  \pm  \sqrt{1} }

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

<u>C</u><u>o</u><u>n</u><u>c</u><u>l</u><u>u</u><u>s</u><u>i</u><u>o</u><u>n</u>

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

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