Problem
Reverse the operations to find the start
A starting number was multiplied by 4, then 50 was added, then the result was divided by 5, ending at 14. We must find the original starting number by reversing each step.
Operations
Your answer
Watch out You must undo the steps in reverse order — start with the last operation (÷5) first, not the first one (×4).
How to solve
Strategy Work Backwards — The end result (14) is given and the start is unknown, which is the classic signal to work backwards. The diagram even labels each inverse operation, so we apply the opposite of each step in reverse order. A quick forward check confirms the answer.
1STEP 1
Undo the divide-by-5
The last forward step divided by 5 to reach 14, so its inverse is multiply by 5. Multiplying 14 by 5 recovers the value before that step.
14 × 5 = 70
Multiplying undoes dividing, so we climb back up from 14 to 70.
3.OA.A.4Work BackwardsMultiplying the final result 14 by 5 gives 70, the value the number had just before the divide-by-5 step.
Why?
The divide-by-5 was the last thing done to reach 14, so undoing that one step gives back exactly the number that went into it.
Why?
Undoing a step means doing its opposite, and the opposite of dividing by 5 is multiplying by 5.
Why?
Multiplying and dividing by the same number are opposite operations that reverse each other.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Undo the add-50
Before dividing, 50 had been added. The inverse of adding 50 is subtracting 50, so take 50 away from 70.
70 - 50 = 20
Subtraction reverses addition, peeling off the 50 that was put on.
3.OA.D.8Work Backwards3STEP 3
Undo the multiply-by-4
The first forward step multiplied the start by 4. The inverse is divide by 4, so divide 20 by 4 to recover the original number.
20 ÷ 4 = 5
Dividing undoes multiplying, returning us to the very first number.
3.OA.A.4Work BackwardsAnswer
5
20 ÷ 4 = 5
Run it forward to check: 5 times 4 is 20, plus 50 is 70, divided by 5 is 14 — exactly the given result. So 5 is correct.
Takeaway
To find a hidden starting number, walk the steps backward and flip each operation — divide becomes multiply, add becomes subtract!
- Undo the divide-by-5
- Undo the add-50
- Undo the multiply-by-4
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested