The ratio of dogs to cats is $5: 3$ The ratio of fish to dogs is $6: 1$
Find the ratio of cats to fish. Give your answer in its simplest form.

Answer

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Answer

$\boxed{\frac{1}{10}}$ is the ratio of cats to fish.

Steps

Step 1 ：Let the number of dogs be 5x and the number of cats be 3x.

Step 2 ：Let the number of fish be 6y and the number of dogs be y.

Step 3 ：Since the number of dogs is the same in both ratios, we can equate them: 5x = y.

Step 4 ：Now we can find the ratio of cats to fish: $\frac{3x}{6y}$.

Step 5 ：Substitute the value of y from step 3: $\frac{3x}{6(5x)}$.

Step 6 ：Simplify the expression: $\frac{3x}{30x}$.

Step 7 ：Cancel out the x terms: $\frac{3}{30}$.

Step 8 ：Simplify the fraction: $\frac{1}{10}$.

Step 9 ：$\boxed{\frac{1}{10}}$ is the ratio of cats to fish.