To solve for the missing numerator in the proportion [tex]\(\frac{?}{108} = \frac{4}{9}\)[/tex], we need to set up an equation and solve for the unknown numerator.
Step 1: Write the proportion as an equation.
[tex]\[
\frac{x}{108} = \frac{4}{9}
\][/tex]
where [tex]\(x\)[/tex] is the missing numerator.
Step 2: To solve for [tex]\(x\)[/tex], we can utilize the property of proportions which states that the cross products of the ratios are equal. This means:
[tex]\[
9x = 108 \times 4
\][/tex]
Step 3: Calculate the right-hand side of the equation:
[tex]\[
9x = 432
\][/tex]
Step 4: Divide both sides of the equation by 9 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{432}{9}
\][/tex]
Step 5: Perform the division to find [tex]\(x\)[/tex]:
[tex]\[
x = 48
\][/tex]
Therefore, the missing numerator is [tex]\(48\)[/tex].
Given the provided options:
- 90
- 45
- 54
- 48
The correct answer is [tex]\(48\)[/tex].
