Question

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 77/... 333

Answer 1

3 or 4

Explanation:

77 has factors 7 and 11

To be reducible, the denominator must have one of these factors too

For the common factor to be 11:

77/3333

7/303

For the common factor to be 7:

77/4333

11/619

For the common factor to be 77:

Answer 2

129

Explanation:

If you want it reduceable to a unit fraction, then the reciprocal would be equal to an integer. Make an equation, "(333+x)/77=y," and you see the positive side is just under 5, so you plug in "5 = y," and get 52 = x. That isn't a 3 digit number, so you plug in "6 = y," and get 129 = x.