Question #fea46

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Question #fea46

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Answer 1 · 2016-09-01T12:33:51

$8 \div 2$ $8 div 2$ is the same as $\frac{8}{2} = 4$ $8/2 = 4$

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!

$2 \div 3 = \frac{2}{3} 20 \div 4 = \frac{20}{4} = 5$ $2 div 3 =2/3 " "20 div 4 = 20/4 = 5$

$5 \div 10 = \frac{1}{2}$ $5 div 10 = 1/2$ It can also be shown as $\frac{5}{10} = \frac{1}{2}$ $5/10 = 1/2$

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

Answer 2 · 2016-09-05T14:57:06

Something to think about!

Explanation:

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

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

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:

$\frac{count}{size indicator of what you are counting} \to \frac{numerator}{denominator}$ $("count")/("size indicator of what you are counting") ->("numerator")/("denominator")$

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
. Tony B Tony B

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

$tan (θ) = \frac{Length of AC = 4}{Length of BC=3} = \frac{4}{3}$ $tan(theta) = ("Length of AC = 4")/("Length of BC=3") = 4/3$

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

$tan (θ) = \frac{4 \div 3}{3 \div 3} = \frac{1.33 ¯ 3}{1}$ $tan(theta)=(4-:3)/(3-:3) = (1.33bar3)/1$

People do not bother to write the 1 so you end up with just $tan (θ) = 1.33 ¯ 3$ $tan(theta)=1.33bar3$

This is actually saying we have $1.33 ¯ 3$ $1.33bar3$ of AC for 1 of BC

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

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

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

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

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