Answer :
Sure! Let's work through the solution step by step.
We need to find all possible ratios of dogs to cats given that there are 24 dogs and 12 cats at a pet daycare.
1. Initial Ratio:
- To find the initial ratio of dogs to cats, we simply use the numbers given: 24 dogs and 12 cats.
- This gives us the ratio 24:12.
2. Simplifying the Ratio:
- To simplify the ratio, we need to find the greatest common divisor (GCD) of 24 and 12. The GCD is the largest number that divides both 24 and 12 without leaving a remainder.
- The GCD of 24 and 12 is 12.
- Now we divide both the number of dogs (24) and the number of cats (12) by their GCD (12) to simplify the ratio.
- For dogs: [tex]\(24 \div 12 = 2\)[/tex]
- For cats: [tex]\(12 \div 12 = 1\)[/tex]
- The simplified ratio is 2:1.
3. Possible Ratios:
- From the steps above, we have two possible ratios: the original one and the simplified one.
- So, the possible ratios of dogs to cats are 24:12 and 2:1.
In conclusion, the possible ratios of dogs to cats that can be made with 24 dogs and 12 cats at the pet daycare are 24:12 and 2:1.
We need to find all possible ratios of dogs to cats given that there are 24 dogs and 12 cats at a pet daycare.
1. Initial Ratio:
- To find the initial ratio of dogs to cats, we simply use the numbers given: 24 dogs and 12 cats.
- This gives us the ratio 24:12.
2. Simplifying the Ratio:
- To simplify the ratio, we need to find the greatest common divisor (GCD) of 24 and 12. The GCD is the largest number that divides both 24 and 12 without leaving a remainder.
- The GCD of 24 and 12 is 12.
- Now we divide both the number of dogs (24) and the number of cats (12) by their GCD (12) to simplify the ratio.
- For dogs: [tex]\(24 \div 12 = 2\)[/tex]
- For cats: [tex]\(12 \div 12 = 1\)[/tex]
- The simplified ratio is 2:1.
3. Possible Ratios:
- From the steps above, we have two possible ratios: the original one and the simplified one.
- So, the possible ratios of dogs to cats are 24:12 and 2:1.
In conclusion, the possible ratios of dogs to cats that can be made with 24 dogs and 12 cats at the pet daycare are 24:12 and 2:1.
