When dividing for example 4 by 2 you can do this strait off. So is there a way can do this with fractions?

It takes quite a while to explain what happens but the actual process is very quick once understood

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#color(green)("Point 1")#

The reason #4 divide 2# can be done strait off is that they are both of the same unit size. The 'unit size #color(blue)("'when viewed this way'")# is how many of what you are counting it takes to make a whole.

So if you have #1/2# then the count is 1 and the unit size is such that it takes 2 of them to make a whole.

If you have #2/3# then the count is 2 and the unit size is such that it takes 3 of them to make a whole.

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#color(green)("Point 2")#

When counting 'the normal way' such as 1, 2 , 3 and so on, you can write them as: #1/1, 2/1, 3/1 # The bottom number (denominator) is how many of what you are counting it takes to make a whole of something. This is why #4 divide 2# can be done strait off!!!

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#color(green)("Using the idea")#

#3/8 divide 2#

Write as:

#3/8 divide 2/1#

#color(blue)("if you make the unit sizes the same you can then divide the counts directly"#

When dividing you are doing so with counts. In this case you can not divide the count of 2 directly into the count of 3 as the unit sizes are different. One is of unit size 8 and the other of unit size 1.

Lets look at how to change #2/1# into the same unit size as #3/8#

If we multiply #2/1# by 1 we do not change its value. There are many ways of writing 1. Suppose we chose to write it as #8/8#

Then #2/1 times 1 -> 2/1 times 8/8#

But #2/1 times 8/8 = 16/8#

So we can write

#3/8 divide 16/8#

This is exactly the same as #3 divide 16 -> 3/16#