What number must replace x
and y
for the three fractions to become equivalent?
6/14 = x/7 = 24/y
To find the value of x and y that will make all three fractions equivalent, we need to find a common denominator for the fractions 14, 7, and y.
The smallest common denominator for 14 and 7 is 14, so the equivalent fraction for 6/14 is 6/14 * (14/14) = 6/14 * 1 = 6/14.
To make the second fraction equivalent to the first, we need to have x/7 = 6/14. Cross-multiplying, we get 14x = 6 * 7 = 42. Dividing both sides of the equation by 14, x = 42/14 = 3.
Now, to find the value of y, we need to make the third fraction equivalent to the first. Since we have already found that x = 3, the third fraction becomes 24/y = 6/14. Again, cross-multiplying, we get 24 * 14 = 6 * y. Simplifying, we have 336 = 6y. Dividing both sides by 6, y = 336/6 = 56.
Therefore, x = 3 and y = 56 will make the three fractions equivalent.