### Instruction: Two friends are playing tic-tac-toe. If Amy wins $\frac{3}{8}$ of the time, Lily wins $\frac{3}{10}$ of the time, and they tie the rest of the time, then what fraction of the time do they tie?### Response: I need to find the fraction of the time that they tie, so I need to add up the fractions of the time that they win and subtract that from 1.
To add fractions, I need to find a common denominator.
The lowest common denominator of 8 and 10 is 40, so I need to multiply the numerator and denominator of the first fraction by 5 and the second fraction by 4.
This gives me $\frac{15}{40}$ and $\frac{12}{40}$ as the fractions of the time that they win.
To add them, I need to add the numerators and keep the same denominator, so I get $\frac{27}{40}$ as the fraction of the time that they win.
To find the fraction of the time that they tie, I need to subtract this fraction from 1, which is the same as $\frac{40}{40}$.
To subtract fractions, I need to subtract the numerators and keep the same denominator, so I get $\frac{40}{40} - \frac{27}{40} = \frac{13}{40}$ as the fraction of the time that they tie.