Working Backwards

Free interactive math game: Working Backwards — Undo the steps. Part of the Addition & Subtraction category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. I thought of a number, multiplied it by 4, then subtracted 41, and got 11. What was the original number?
  2. I thought of a number, multiplied it by 4, then added 4, then subtracted 38, and got 2. What was the original number?
  3. I thought of a number, subtracted 3, then multiplied it by 3, and got 24. What was the original number?
  4. I thought of a number, subtracted 2, then multiplied it by 3, and got 18. What was the original number?

About this exercise

Undoing a chain of operations to recover the number someone started with.

How to solve it

Work from the final result towards the start, reversing each step: addition becomes subtraction, multiplication becomes division.

Worked example

If a number was doubled and then had 3 added to give 21, take away 3 to get 18 and halve it to get 9.

Common mistake

Reversing the operations but keeping the original order. The last thing done must be the first thing undone.