Question

Question #fea46

Answer 1

`8 div 2` is the same as `8/2 = 4`

A fraction is a quicker and easier way of writing a division, especially in the algebra which lies ahead.

Explanation:

Writing a division as a fraction is a more useful way of showing the division. They mean exactly the same thing!

`2 div 3 =2/3 " "20 div 4 = 20/4 = 5`

`5 div 10 = 1/2` It can also be shown as `5/10 = 1/2`

As you work more and more with Algebra you will find that you use the `div` sign less and less, and divisions are shown as fractions.

Answer 2

Something to think about!

Explanation:

`color(brown)("The big question is: does it actually mean divide?")`

`color(green)("I can only leave you with an open question")`

A fraction is something that has been so much a part of my life for so long that I have not really given much thought to this question.

Consider what a fraction is:

`("count")/("size indicator of what you are counting") ->("numerator")/("denominator")`

The size indicator is how many of what you are counting it takes to make a whole.

The line's prime function is to separate the two numbers. Its very existence and agreed format also tells us that we to consider the relationship between the two numbers in a particular way. That we are counting parts of a whole and declaring the size of what we are counting.

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The problem comes from the tendency and convention to disregard something. Let me explain:

It is all to do with ratio and I wish to demonstrate this using a right triangle
.

If you are familiar with a little trig consider the value (ratio) of `tan(theta)` full name of Tangent.

`tan(theta) = ("Length of AC = 4")/("Length of BC=3") = 4/3`

Suppose we were to change the 3 into 1 we have:

`tan(theta)=(4-:3)/(3-:3) = (1.33bar3)/1`

People do not bother to write the 1 so you end up with just `tan(theta)=1.33bar3`

This is actually saying we have `1.33bar3` of AC for 1 of BC

However there is a tendency for people to say divide the 3 into 4 and you get `1.33bar3` which is true but is it what `tan(theta)` is actually declaring. `tan(theta)` is saying that for 1 along you get `1.33bar3` up.

Looking at a fraction, say `1/2`. Divide 2 into 1 and you get 0.5. However, like in the ratio, what is missed out is that it really is `0.5/1` because we have `(1-:2)/(2-:2) = 0.5/1`

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`color(green)("The open question!")`

`color(green)("The problem is that numerically they behave in the same way. So does it mean divide or not?")`