Given the expression:
[tex]\text{ }2\text{ }\frac{1}{4}\text{ - }\frac{6}{4}[/tex]Under the rule of subtracting fractions, we must first transform the mixed number into an improper fraction.
We get,
[tex]\text{ 2}\frac{1}{4}\text{ = }\frac{1\text{ + (2 x 4)}}{4}\text{ = }\frac{1\text{ + 8}}{4}\text{ = }\frac{9}{4}[/tex]Let's now proceed with the subtraction:
[tex]\text{ }2\text{ }\frac{1}{4}\text{ - }\frac{6}{4}\text{ = }\frac{9}{4}-\frac{6}{4}[/tex][tex]\text{ = }\frac{9\text{ - 6}}{4}[/tex][tex]\text{ = }\frac{3}{4}[/tex]Therefore, the difference between 2 1/4 and 6/4 is 3/4.