"1/7 of the buttons in a box are black and the rest are white. "
total → 7u black → 1u white → 7u - 1u = 6u
"There are 180 white buttons."
6u → 180 1u → 180 ÷ 6 = 30
total in the end → 180 + 78 + 30 = 288
fraction of white → 180 / 288 (divide by 2) = 90 / 144 (divide by 2) = 45 / 72 (divide by 3) = 15 / 24 (divide by 3) = 5 /8