7 13/24 : 1 1/48 * 2 1/4 = ?

Convert the mixed numbers to improper fractions:
$$7 \frac{13}{24} = \frac{7 \cdot 24 + 13}{24} = \frac{168 + 13}{24} = \frac{181}{24}$$
$$1 \frac{1}{48} = \frac{1 \cdot 48 + 1}{48} = \frac{48 + 1}{48} = \frac{49}{48}$$
$$2 \frac{1}{4} = \frac{2 \cdot 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$$
Now the expression is:
$$\frac{181}{24} : \frac{49}{48} \cdot \frac{9}{4}$$
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the expression as:
$$\frac{181}{24} \cdot \frac{48}{49} \cdot \frac{9}{4}$$
Now, multiply the fractions:
$$\frac{181 \cdot 48 \cdot 9}{24 \cdot 49 \cdot 4} = \frac{181 \cdot 2 \cdot 9}{49 \cdot 4} = \frac{181 \cdot 18}{49 \cdot 4} = \frac{3258}{196}$$
Now convert the improper fraction to a mixed number:
$$\frac{3258}{196} = 16 \frac{3258 - 16 \cdot 196}{196} = 16 \frac{3258 - 3136}{196} = 16 \frac{122}{196} = 16 \frac{61}{98}$$

Answer: 16 61/98