You have 33 dogs and 4 kennels. Divide the dogs up evenly so the same number of dogs is in each kennel. I was told to show work and that I could not count part of a dog. Please help. Thank you.

Well this is my thinking. The factors of 33 are as follows:

1 x 33
3 x 11

Therefore, you wouldn't be able to fill all 4 kennels if you used all the dogs. The only thing that makes sense to me is to not put one of the dogs in the kennel (which gives you 32 dogs):

4 x 8 = 32

So if you put 8 dogs per kennel, you have the same number of dogs in each kennel.

only use 3 of the available kennels?

8 remainder of 1

To evenly divide 33 dogs into 4 kennels, you can follow these steps:

1. Start by determining the maximum number of dogs that can be evenly divided among the kennels. Divide the total number of dogs (33) by the number of kennels (4).
33 รท 4 = 8.25

2. Since you cannot count a fraction of a dog, you need to find the largest whole number that is less than or equal to 8.25. In this case, it is 8.

3. Multiply this number by the number of kennels to determine the total number of dogs that will be allocated.
8 x 4 = 32

4. Now, you need to distribute the remaining dogs. Subtract the total number of dogs allocated from the original number of dogs.
33 - 32 = 1

5. Since you have 1 dog remaining, you can distribute it among the existing kennels, starting from the first kennel. This means each of the kennels will have 8 dogs, except for one kennel, which will have 9 dogs.

So the distribution will be:
- Kennel 1: 9 dogs
- Kennel 2: 8 dogs
- Kennel 3: 8 dogs
- Kennel 4: 8 dogs

This ensures an equal distribution of dogs among the kennels, except for one kennel that has an extra dog as the remainder.