To determine the missing denominator in the fraction equation [tex]\(\frac{3}{2} = \frac{18}{?}\)[/tex], we proceed with the following steps:
1. Start with the given equation:
[tex]\[
\frac{3}{2} = \frac{18}{?}
\][/tex]
2. Denote the missing denominator by [tex]\(x\)[/tex]:
[tex]\[
\frac{3}{2} = \frac{18}{x}
\][/tex]
3. Use cross-multiplication to solve for [tex]\(x\)[/tex]. The principle of cross-multiplication states that if two fractions are equal, the product of the numerator of one fraction and the denominator of the other fraction will be equal to the product of the numerator of the second fraction and the denominator of the first fraction:
[tex]\[
3 \cdot x = 2 \cdot 18
\][/tex]
4. Perform the multiplication on the right-hand side:
[tex]\[
3x = 36
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 3:
[tex]\[
x = \frac{36}{3}
\][/tex]
6. Calculate the division:
[tex]\[
x = 12
\][/tex]
Therefore, the missing denominator value is [tex]\(12\)[/tex].
So the answer is: 12
