Final answer:
To make the fractions 7/12 and ?/48 equivalent, we create a proportion and solve for the missing numerator, which is found to be 28 after cross-multiplying and dividing both sides by 12. The second fraction is therefore 28/48, which can be reduced to 7/12, confirming the fractions are equivalent.
Step-by-step explanation:
The question asks to find the number that would make the fractions 7/12 and ?/48 equivalent. To solve this, we can create a proportion where the two fractions are set equal to each other. Since we are looking for the missing numerator in the second fraction, we set up the proportion as follows: 7/12 = x/48.
To find the value of x, we can cross-multiply. This means we multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the x in the numerator of the second fraction. Therefore, we have 7 * 48 = 12 * x. Simplifying, we get 336 = 12x.
To isolate x and solve for it, we need to divide both sides of the equation by 12: 336 / 12 = 12x / 12. This gives us x = 28. Therefore, the number that makes the fractions equivalent is 28, so the second fraction is 28/48.
We can also check this answer by reducing the second fraction to its simplest form. Since both 28 and 48 are divisible by 4, we can divide the numerator and the denominator by 4 to get 7/12, which verifies that the fractions are indeed equivalent.