No, she is not correct; you need to make all of the denominators the same by finding the highest common factor.
The highest common factor of all of these is 28, so you must multiply each numerator by however much you multiplied the denominators. So:
1/7 x 4 = 4/28
1/14 x 2 = 2/28
2/28 x 1 = 2/28
Now you need to add all of these, which would be 6/28.
6/28 is less than half, so she is not correct.
Hope this helps