Let's denote the first number as xxx and the second number as yyy. According to the problem:

45 of x=23 of y\frac{4}{5}\text{ of }x=\frac{2}{3}\text{ of }y54​ of x=32​ of y

This can be written as:

45x=23y\frac{4}{5}x=\frac{2}{3}y54​x=32​y

To find the ratio xy\frac{x}{y}yx​, solve for xxx in terms of yyy:

45x=23y\frac{4}{5}x=\frac{2}{3}y54​x=32​y

Multiply both sides by 54\frac{5}{4}45​:

x=23y×54=2×53×4y=1012y=56yx=\frac{2}{3}y\times \frac{5}{4}=\frac{2\times 5}{3\times 4}y=\frac{10}{12}y=\frac{5}{6}yx=32​y×45​=3×42×5​y=1210​y=65​y

Therefore,

xy=56\frac{x}{y}=\frac{5}{6}yx​=65​

Final answer:

The ratio of the first number to the second number is 5:6\boxed{5:6}5:6​.