This goes right back to the idea of cancelling (reducing ?) and why it works.

My diagram shows a rectangle split into 12 parts with 3 shaded.

Then I've split the same rectangle into just 4 parts with one shaded.

so

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.

http://www.mathsisfun.com/equivalent_fractions.html

Bob

]]>Well, like that, if we are working only on one side of an equation, if we do something to that side of the equation we have to do the opposite or inverse of that action for that side of the equation to still hold true. Simple example: if our equation was 5+5=10

If we decided to subtract 3 from the first side we'd get 5+5-3=10, well that's not true , but as long as we did the opposite of that our equation would still be true. 5+5-3+3=10, now it's true again.

Same goes for with the fractions, in essence when looking at

All we are doing is dividing that entire side of the equation, and at the same time multiplying the entire side of the equation by 4. Like this: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

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.

]]>You mean do this?

]]>Reduce the eights by what?

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