To find the ratio of the number of children who own a dog to the total number of children in the kindergarten class, we need to follow these steps:
1. Determine the number of children who own a dog:
The problem states that 10 children in the class own a dog.
2. Determine the number of children who do not own a dog:
According to the problem, 14 children in the class do not own a dog.
3. Calculate the total number of children in the kindergarten class:
We add the number of children who own a dog to the number of children who do not own a dog:
[tex]\[
10 + 14 = 24
\][/tex]
So, there are 24 children in total in the class.
4. Find the ratio of the number of children who own a dog to the total number of children:
The ratio is given by the fraction where the numerator is the number of children who own a dog, and the denominator is the total number of children:
[tex]\[
\frac{10}{24}
\][/tex]
5. Simplify the fraction:
To simplify [tex]\(\frac{10}{24}\)[/tex], we find the greatest common divisor (GCD) of 10 and 24. The GCD of 10 and 24 is 2.
We divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{10 \div 2}{24 \div 2} = \frac{5}{12}
\][/tex]
Therefore, the simplified fraction of the ratio of the number of children who own a dog to the total number of children in the class is [tex]\(\frac{5}{12}\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{\frac{5}{12}}
\][/tex]
