Ratios can be expressed in writing in various ways. Assets-to-equity can also be written as assets: equity OR assets/equity, for example. Let's use the notation that people tend to be more familiar with: assets/equity.
So now we've reformatted the assets-to-equity ratio to be: Assets / Equity = 40%.
The 40% can also be expressed in different forms. For example, 40% could be written as 40/100. If we move the decimal point to the left for both the numerator and denominator, it would be 0.40/1.00.
Reformatting the assets-to-equity ratio again, we have: Assets / Equity = 0.40 / 1.00.
Looking at just the *numerators* on both sides of the equal sign, we know that Assets = 0.40
Looking at just the *denominators* on both sides of the equal sign, we know that Equity = 1.00
Now let's put the second ratio, equity-to-assets, into the same format: equity/assets.
Since we've said that Assets = 0.40, and Equity = 1.00, we can plug those numbers into the equity-to-assets ratio: Equity / Assets = 1.00 /.40.
Doing the division, we now have: Equity / Assets = 1.00 /.40 = 2.50.
