To determine what denominator would make the ratios \( \frac{213}{21} \) and \( \frac{49}{?} \) proportional, you need to set up the proportion:
\[ \frac{213}{21} = \frac{49}{?} \]
To solve for the unknown denominator (let's call it \( x \)), you can cross-multiply:
\[ 213 \cdot x = 21 \cdot 49 \]
Now, calculate \( 21 \cdot 49 \):
\[ 21 \cdot 49 = 1029 \]
Now, the equation becomes:
\[ 213x = 1029 \]
Next, solve for \( x \):
\[ x = \frac{1029}{213} \]
Calculating this gives:
\[ x = 4.828 \]
Therefore, to make the ratios proportional, you need a denominator of approximately \( 4.828 \). If you're looking for a whole number, it might not be applicable; if you require an exact match with integer values, double-check the initial ratios and context for any specific needs (like nearest integers or rounding).