To find a denominator that makes the ratios \( \frac{213}{49} \) and \( \frac{a}{b} \) proportional, we need to find \( b \) such that:
\[ \frac{213}{49} = \frac{a}{b} \]
This means we can cross-multiply:
\[ 213b = 49a \]
To make the values easy to work with, let's solve for \( b \):
\[ b = \frac{49a}{213} \]
So, to find a value for \( b \) that keeps the ratios \( \frac{213}{49} \) and \( \frac{a}{b} \) proportional, you can select any value for \( a \), and then calculate \( b \) using the formula above.
For example, if \( a = 49 \):
\[ b = \frac{49 \times 49}{213} = \frac{2401}{213} \approx 11.29 \]
If \( a = 213 \):
\[ b = \frac{49 \times 213}{213} = 49 \]
Thus, any value of \( b \) calculated from the ratio will maintain the proportionality. Just choose a value for \( a \) and plug it into the equation to calculate \( b \).
Determine any specific values you’d like to use for \( a \) or \( b \), and I can help compute the corresponding results!