Problem
The mistake was adding 3 4/5 to get 7 5/7. To find the hidden number, do the opposite of adding: subtract 3 4/5 from 7 5/7.
If a step added something, undoing that step means subtracting the same amount back off — that is just running the action in reverse.
5.NF.A.2Work BackwardsThe hidden number is found by subtracting 3 4/5 from 7 5/7.
The mistake was adding 3 4/5, and taking that same amount away undoes the adding.
What is left once the mistake is undone is the number that stood there before it, which is what the correct calculation needs.
The wrong result is the hidden number together with the amount wrongly added, and nothing else.
Write both mixed numbers as fractions over a common denominator of 35, then subtract: 7 5/7 = 54/7 = 270/35 and 3 4/5 = 19/5 = 133/35.
Sevenths and fifths are different-sized pieces, so I cut both into 35ths — the smallest size both fit into — and then the numerators subtract directly.
5.NF.A.1Identify SubproblemsNow subtract properly: 137/35 - 133/35 = 4/35.
Both amounts are now in 35ths, so subtracting is just counting how many 35-pieces are left after taking the others away.
5.NF.A.1Identify SubproblemsWhen a wrong answer comes from adding instead of subtracting, undo the adding to find the secret number — then do the subtraction the right way.