What denominator for 213=49? would make these ratios proportional?(1 point) $$
To make the ratios proportional, we need to find the common denominator for the two fractions.
The fraction 213/49 simplifies to 3/7.
To find the common denominator, we need to find the least common multiple (LCM) of 7 and the denominator. Since 7 is a prime number, the LCM of 7 and any number is the product of the numbers.
Therefore, the denominator that would make these ratios proportional is 7.
Nigel is selling candy bars for his outdoor club. He is averaging 4 bars every 3 days. If he continues at this rate, how many days will it take to sell his box of 36? Your answer should be a whole number.(1 point)
To make two ratios proportional, we need the cross products (product of the numerator of one ratio and the denominator of the other ratio) to be equal.
In this case, the given ratio is 213/49.
To make it proportional, we need to find a denominator that, when multiplied by the numerator of the other ratio, gives the same result as when the numerator of the given ratio is multiplied by the denominator of the other ratio.
Let's assume the missing denominator is x.
The cross product for the given ratio (213/49) with the missing denominator x would be:
213 * x
The cross product for the other ratio (numerator: ? and denominator: 49) with the given denominator is:
? * 49
To make the ratios proportional, we need the cross products to be equal:
213 * x = ? * 49
Since it is not clear what the numerator of the other ratio is given, we cannot determine the exact denominator that would make the ratios proportional.
To find the denominator that would make the ratios proportional, we need to compare the ratio 213:49 with a second ratio that is proportional to it.
The ratios are proportional if they have the same value when simplified. To simplify a ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD).
In this case, the GCD of 213 and 49 is 1 (since they are both prime numbers). Therefore, the simplified form of the ratio is 213:49.
To find the denominator that would make the two ratios proportional, we need to find a number that is a multiple of 49. A multiple of a number is obtained by multiplying that number by any integer.
For example, if we multiply 49 by 2, we get 98. So, the ratio 213:98 is proportional to 213:49 because they have the same value when simplified.
Therefore, a denominator of 98 would make the ratios proportional: 213/98 = 49/98.