What denominator for 213=49? would make these ratios proportional?
To make these ratios proportional, we need to find a common denominator for the fractions.
The given equation is 213 = 49, which is not a fraction and doesn't have a denominator. Therefore, the question about finding a denominator for this equation is invalid.
If you meant to ask about finding a denominator for fractions such as 213/denominator = 49/denominator, then the answer would be any nonzero denominator would work, as long as it is the same for both fractions.
To determine the denominator that would make the ratios proportional, you can compare the two ratios and find a common denominator.
The given ratio is 213/49. To find a proportional ratio, you need to multiply both the numerator and denominator by the same factor. Let's call this factor "x."
So the proportional ratio can be written as (213x)/(49x).
Now you need to find the value of "x" that makes the two ratios equivalent. This can be done by finding the greatest common divisor (GCD) of the original denominator (49) and the new denominator (49x).
Since 49 is a prime number, the GCD would be 49. Thus, the denominator for the proportional ratio that would make these ratios proportional is 49.
To determine the denominator that would make the ratios proportional, we need to find a common ratio between the two ratios.
The given ratio is: 213/49.
To make the ratios proportional, we need to find a common ratio between this ratio and an unknown ratio with a different denominator. Let's call this unknown denominator "x". So, the ratio with the unknown denominator would be: 213/x.
To find a common ratio, we set up a proportion by equating the ratios:
213/49 = 213/x
Now, we cross-multiply:
213 * x = 49 * 213
To solve for "x", we divide both sides of the equation by 213:
x = (49 * 213) / 213
Simplifying the expression:
x = 49
Therefore, the denominator that would make the ratios proportional is 49.