Working Backward with Operations (Grade 5)
Sometimes you know the result of a chain of operations and need the starting number — so you undo each step in reverse order using inverse operations (subtraction undoes addition, division undoes multiplication). "A number, times 2, plus 3, equals 11" → undo +3 (11 − 3 = 8), then undo ×2 (8 ÷ 2 = 4).
Understanding working backward with operations
Sometimes you know the result of a chain of operations and need the starting number — so you undo each step in reverse order using inverse operations (subtraction undoes addition, division undoes multiplication). "A number, times 2, plus 3, equals 11" → undo +3 (11 − 3 = 8), then undo ×2 (8 ÷ 2 = 4).
Key Idea
Sometimes you know the result of a chain of operations and need the starting number — so you undo each step in reverse order using inverse operations (subtraction undoes addition, division undoes multiplication). "A number, times 2, plus 3, equals 11" → undo +3 (11 − 3 = 8), then undo ×2 (8 ÷ 2 = 4).
Seeing it in action
Worked example
A number is multiplied by 2, then 3 is added, giving 11. Find it.
Undo in reverse: 11 − 3 = 8, then 8 ÷ 2 = 4.
Undo the operations in reverse order.
Try a few
×3 then −1 gives 14. Start?
+5 then ×2 gives 20. Start?
÷2 then +4 gives 9. Start?
Make the Target
A calm operations game for choosing operators, evaluating expressions, and placing brackets.
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