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This may seem like a wierd question, but here I go : If I have 8/3 . 8/5 = 64/15 why can't I reduce my two 8's at the beginning ? I can reduce my fractions diagonaly or I can reduce the number above the fraction sign and the other one below it. But why can't I do it in a straight line ? Would it be to hard to explain and I have to take it like it is ? Thank you (I like to understand how things works ^^)
One way of looking at it is
You end up with a 4 on the top and on the bottom. You can cancel them.
When you do the other one.
There is nothing to cancel.
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The way I look at it is like this, much like when you are working in algebra, if you do something to one side of an equation you have to do it to the other side of an equation for it to still be equal.
and at the same time
With what you are trying to do, you are dividing the same side of the equation by 8, twice. Going back to my simple example, 5+5=10, your action would look something like this, 5+5-3-3=10. And that just can't work, if you do something to a side, you have to do the opposite to keep the equation equal.
So, what you did would look like this:
And that equation is definitely not the same as
The twelve parts have been collected together into groups of 3 to show that 3 parts in 12 is the same as 1 part in 4
All cancelling relies on this.
If there's a factor of the top that is also a factor of the bottom, you may cancel it. But cancelling a factor of the top with another factor of the top would change the value of the fractions completely.
this is ok:
because the eights are one on the top and one on the bottom.
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