in my house, the ratio of dogs to fish is 1:10. the ratio of fish to cats is 6:1. What is the ratio of dogs to cats?

Ratio represents partial data as some multiplies from numerator and denominator are lost due to simplification. You can assume them to be variables.

The ratio of dogs to cats is 3:5

How to get real quantity of ratio of first quantity to second quantity = a:b?

We actually cannot get real quantities but we can use variables to partially get the information of how much their quantities were.

I said 'partially' since we don't get real values but with variables only.

Since the ratio is a:b, thus let the cancelled multiple during simplification was x.

Then we have:

First quantity = ax

Second quantity = bx

How to calculate the ratio of dogs to cats?

It is given that:

Ratio of dogs to fish = 1:10

Then let number of dogs = 1x = x and number of fishes = 10x

Similarly,

Ratio of fish to cats = 6:1

Then let the multiple was y, then

Number of fishes = 6y,

Number of cats = 1y = y

But we have number of fishes = 10x and 6y both

Since number of fishes is constant, thus, they are equal. Or

[tex]10x = 6y\\\dfrac{x}{y} = \dfrac{6}{10} = \dfrac{3}{5}\\[/tex]

The ratio of dogs to cats = [tex]\dfrac{\text{Numbers of dogs}}{\text{Number of cats}} = \dfrac{x}{y} = \dfrac{3}{5}[/tex]

Thus, the ratio of dogs to cats is 3:5

Learn more about ratio here:

https://brainly.com/question/13513438