Final answer:
Anya's dog ate a total of 1 ½ cups of dog food over the course of the day, after converting 3/4 cup and 5/6 cup to have a common denominator and adding them together.
Step-by-step explanation:
To find out how much Anya's dog ate over the course of the day, we need to add the amounts of dog food fed in the morning and in the evening. Anya fed her dog 3/4 cup in the morning and 5/6 cup in the evening. To add these two fractions, they must have a common denominator.
The least common denominator for 4 and 6 is 12. We convert the fractions to have the common denominator of 12:
- Morning: (3/4) × (3/3) = 9/12
- Evening: (5/6) × (2/2) = 10/12
Now we can add the equivalent fractions:
9/12 + 10/12 = 19/12
19/12 cups is greater than 1 cup, so we can also express it as a mixed number:
19/12 = 1 ½ cups (1 whole cup plus ½ cup).
Therefore, Anya's dog ate a total of 1 ½ cups of dog food over the course of the day.