Problem
Undo a wrong fraction operation to recover the start
You were supposed to subtract 4/11 from a number, but accidentally added 4/11 and got 10/11. First recover the original number, then do the correct subtraction.
Fractions
Your answer
Watch out Recovering 6/11 undoes the mistake, but stopping there and reporting 6/11 as the final answer skips the correct subtraction the problem still asks for.
How to solve
Strategy Work Backwards — The end result of the wrong calculation is given, so work backwards: undo the mistaken addition to recover the original number, then perform the correct subtraction.
1STEP 1
Recover the original number
Undo the mistaken addition by subtracting it back: 10/11 - 4/11 = 6/11.
10/11-4/11=6/11
Working backwards undoes the wrong step by doing its opposite.
4.NF.B.3Work BackwardsThe original number is 10/11 minus 4/11, which is 6/11.
Why?
The mistake reached 10/11 by adding 4/11 onto the number, so taking that same 4/11 back off 10/11 hands the number back.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
Both 10/11 and 4/11 measure the same size of piece, an eleventh, so the subtraction is just 10 of those pieces take away 4 of them.
Why?
10/11 is exactly ten 1/11 pieces added up and 4/11 is four of the very same pieces, so removing four of them from ten leaves six pieces, which is 6/11.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
2STEP 2
Do the correct calculation
The correct operation subtracts 4/11 from the original number: 6/11 - 4/11 = 2/11.
6/11-4/11=2/11
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
4.NF.B.3Identify SubproblemsAnswer
2/11
6/11-4/11=2/11
Check: original 6/11 plus 4/11 really is 10/11 (matches the mistake), and 6/11 minus 4/11 is 2/11. The correct answer 2/11 is smaller than the wrong result 10/11, which makes sense since subtracting should give less than adding.
Takeaway
This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
- Recover the original number
- Do the correct calculation
Where next?
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