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## Homework Statement

A person has come to a world full of pets. He notices right away that dogs are the most prevalent of all pets. But that's not all. He notices these 8 ratios:

Dog:Cat = 5:1

Dog:Rodent = 1:5

Dog:Lizard = 1:3

Dog:Snake = 2:1

Dog:Turtle = 1:3

Dog:Alligator = 3:1

Dog:Crocodile = 7:1

Dog:Bird = 1:10

What are the other ratios based on these 8 ratios

## Homework Equations

$$\frac{\frac{1}{a:b}}{a*\frac{1}{c:d}} = b:ad$$

where

a = antecedent of first ratio

b = consequent of first ratio

c = antecedent of second ratio

and

d = consequent of second ratio

## The Attempt at a Solution

Let's do the Cat:Rodent ratio first

$$\frac{\frac1 5}{5*\frac 5 1}$$

Thus the Cat:Rodent ratio is 5:25 or 1:5

But this doesn't seem right. If cats are 5 times less prevalent than dogs, how can the Cat:Rodent ratio equal the Dog:Rodent ratio? Surely the Cat:Rodent ratio should be 1:25

So what is wrong with my ratio calculating formula that is based on 2 known ratios?

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