Final answer:
To make the fractions (4/10) and (40/?) equal, the missing denominator should be 100 because the numerator 40 is 10 times greater than 4, so the denominator must be 10 times greater than 10.
Step-by-step explanation:
The question asks which number will make the two fractions equivalent: (4/10) = (40/?). To solve for the missing number, we must ensure that both fractions have the same value. Since the first fraction is 4/10, and the numerator of the second fraction is 40, which is 10 times greater than 4, we need to make the denominator 10 times greater than 10 to keep the fractions equal. Therefore, the denominator of the second fraction must be 100, making the fractions equal as (4/10) = (40/100). This is a clear example of creating a proportion by setting two ratios equal to one another and ensuring that the operation performed on the numerator is also performed on the denominator to maintain equality.