What is the correct way to explain the difference between 3 1/4 and 3.25%

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The terms used to identify `3 1/4` and `3.25` would be "mixed number" (which is a whole number and a fraction) and "decimal fraction," respectively. The two are equal to each other.

`3 1/4=3.25`

However, whe you add the percentage sign to the `3.25` 

this changes the decimal fraction from...

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The terms used to identify `3 1/4` and `3.25` would be "mixed number" (which is a whole number and a fraction) and "decimal fraction," respectively. The two are equal to each other.

`3 1/4=3.25`

However, whe you add the percentage sign to the `3.25` 

this changes the decimal fraction from 3.25 to

`3.25/100` as the symbol % means "out of 100"

To convert this back to a decimal fraction do the division:

`3.25% = 0.0325`

To compare your new decimal fraction to a standard fraction you would simplify it. It is no longer a mixed number as it is smaller than 1 so there is no whole number:

`0,0325= 13/400` in its simplified form.

So to explain the difference -

A percentage sign means that a number must be divided by 100 as % (percent) means "out of 100" so the difference between `3 1/4 and 3.25%` is that the decimal fraction must be over 100 and `3.25/100`  is not equivalent to `3 1/4`

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