Sally runs an animal rescue company that allows families to adopt homeless pets. Last month, 2/3 of the adopted animals were dogs, 1/4 of were cats, and the rest were rabbits. Which number represents the part of the adoptions that were rabbits? (Desmos Calculator: Ctrl + select to open in a new tab) (1 point) Responses 112 1 over 12 512 5 over 12 1112 11 over 12 37

Answer 1

To determine the fraction of the adopted animals that were rabbits, we first need to account for the portions of the adoptions that were dogs and cats.

1. The fraction of animals that were dogs is \( \frac{2}{3} \).
2. The fraction of animals that were cats is \( \frac{1}{4} \).

Next, we add these two fractions together to find out how many of the adoptions were either dogs or cats:

\[ \frac{2}{3} + \frac{1}{4} \]

To add these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12. We can convert both fractions:

\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \] \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \]

Now we can add the two fractions:

\[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \]

This means that \( \frac{11}{12} \) of the adopted animals were either dogs or cats. To find the fraction that represents rabbits, we can subtract this from the whole (which is 1):

\[ 1 - \frac{11}{12} = \frac{1}{12} \]

Thus, the fraction of the adoptions that were rabbits is \( \frac{1}{12} \).

Therefore, the final answer is:

1 over 12