Final answer:
The ratio of birthday cards to thank you cards is 4:7, where the box contains 4 birthday cards and 7 thank you cards.
Step-by-step explanation:
The question asks for the ratio of birthday cards to thank you cards in a given box. To find this ratio, you compare the number of birthday cards to the number of thank you cards. In the box, there are 4 birthday cards and 7 thank you cards. Therefore, the ratio of birthday cards to thank you cards is 4:7. This ratio simply compares the two amounts as a pair of numbers, separated by a colon, indicating how many times the first number contains the second. It does not imply any subtraction, addition, or other mathematical operations.