Question

How do I find the quotient of 3/8 and 2?

Answer 1

Another perspective!!!

Explanation:

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`