A man won a lotto jackpot and he spent 2/5 of the money on luxury cars and 1/4 on buying a house. What fraction of his lotto earnings is remaining?

Step 1: Calculate the total fraction of money spent. The man spent $\frac{2}{5}$ on luxury cars and $\frac{1}{4}$ on a house. To find the total fraction spent, add these two fractions: $Total spent = \frac{2}{5} + \frac{1}{4}$ Find a common denominator, which is 20. $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$ Now, add the fractions: $Total spent = \frac{8}{20} + \frac{5}{20} = \frac{8+5}{20} = \frac{13}{20}$

Step 2: Calculate the fraction of money remaining. The total lotto earnings can be represented as 1 (or $\frac{20}{20}$). Subtract the total fraction spent from 1: $Remaining fraction = 1 - \frac{13}{20}$ $Remaining fraction = \frac{20}{20} - \frac{13}{20} = \frac{20-13}{20} = \frac{7}{20}$

The fraction of his lotto earnings remaining is $\boxed{\frac{7}{20}}$.