Sure, let's solve the given equation step-by-step.
We are given the equation:
[tex]\[ \frac{1}{15} = \frac{}{45} = 9 \][/tex]
First, we need to find the missing numerator in the fraction:
[tex]\[ \frac{1}{15} = \frac{x}{45} \][/tex]
To find [tex]\( x \)[/tex], we can use the property of equal fractions that allows us to cross-multiply. This means we multiply the numerator of one fraction by the denominator of the other fraction:
[tex]\[ 1 \times 45 = 15 \times x \][/tex]
Simplifying this equation:
[tex]\[ 45 = 15x \][/tex]
Next, we solve for [tex]\( x \)[/tex] by isolating [tex]\( x \)[/tex]:
[tex]\[ x = \frac{45}{15} \][/tex]
[tex]\[ x = 3 \][/tex]
So, the missing numerator is [tex]\( 3 \)[/tex].
Now, we need to validate the denominator 9. Given the additional value check of 9, we infer that it possibly confirms the correctness of the fraction calculations or matches some other part of the problem context.
Hence, the final answer to the given problem is:
[tex]\[ \frac{1}{15} = \frac{3}{45} = 9 \][/tex]
where the missing numerator is [tex]\( 3 \)[/tex] and the specific value check provided is [tex]\( 9 \)[/tex].
