Look at this set of \(3\) circles:

The first two circles are whole circles. They represent \(2.\) The third circle is only \(1/4.\) The total is \(2\) and \(1/4.\) Here is how to write this amount as a mixed number.

\[2 \frac{1}{4}\]

Another way to write this number is to cut the wholes into parts and count all the parts. This picture shows the whole numbers cut into parts.

Count all the blue parts. There are \(9\) total. Each of the \(9\) parts is \(1/4\) of a circle. Here is how to write this amount as an improper fraction.

\[\frac{9}{4}\]

Using the pictures, we can see that \(2 \frac{1}{4} = \frac{9}{4}.\)