Can someone tell me how to divide fractions like the equation 1 1/2 divided by 2 1/4

To divide a fraction BY a fraction ....flip the denominator and MULTIPLY

1 1/2 = 3/2       2 1/4 = 9/4

3/2  /  9/4     =    3/2  *   4/ 9   = 12/18 = 2/3

Multiply:

First, simplify the mixed numbers to a fraction. This can be accomplished by multiplying the whole number by the number beneath the fraction sign and adding it to the number on top of the fraction sign. This number would now be your numerator over the original denominator. For example, $1 {1 \over 2}$ would be $(1 \times 2) + 1$. This means that the improper fraction, in this case, the product would be ${3 \over 2}$. 

Repeat this to the other number, so you would have $9 \over 4$. To multiply fractions, you multiply the numerators and the denominators. So, in this case, ${ 3 \over 2 }\times {9\over4} =\color{brown}\boxed{{ 27\over 8}}$.

To divide fractions, you need to multiply by the reciprocal. To get the reciprocal, you swap the numerator and the denominator of the SECOND fraction ONLY. In this case, ${3 \over 2 } \div {9\over4}={3\over2}\times {4\over9}$. To multiply both these fractions, you do as stated above, and you recieve $12 \over 18$ or $\color{brown}\boxed{2 \over3}$