If the denominator of 4/7 is increased by a number and the numerator is doubled, the result is 1. find the number.

If the denominator of 4/7 is increased by some number x, then we have 4/(7+x)

If the numerator is doubled, then we now have 8/(7+x) because 4*2 = 8

Set that new fraction 8/(7+x) equal to 1 and solve for x

8/(7+x) = 1
8 = (7+x)*1 multiply both sides by (7+x)
8 = 7+x
7+x = 8
x+7 = 8
x = 8-7 ... subtract 7 from both sides
x = 1

1

(note: 4/7 will turn into 8/8 after adding the number 1 to the denominator and doubling the numerator. The fraction 8/8 reduces to 1)