Final answer:
The numbers that must replace x and y for the fractions to become equivalent are 3 for x and 56 for y, making the fractions 6/14, 3/7, and 24/56 equivalent.
Step-by-step explanation:
To determine what numbers must replace x and y for the three fractions to become equivalent, we need to solve the equation 6/14 = x/7 = 24/y. We can start by cross-multiplying to find the values of x and y. For x, we multiply 6 by 7, and for y, we multiply 24 by 14 and then divide by 6.
The calculation for x is as follows:
x = (6/14) × 7 = 3, since 6 divided by 2 equals 3 and 14 divided by 2 equals 7, and then 3 times 7 equals 3.
The calculation for y will be:
y = 24 × (14/6) = 24 × (7/3) = 56, since 14 divided by 2 equals 7 and 6 divided by 2 equals 3, and then 24 times 7 divided by 3 equals 56.
The values are x = 3 and y = 56. Now, the fractions 6/14, 3/7, and 24/56 are all equivalent.