Operations & Word Problems

Problem

Undo a wrong fraction operation to recover the start

You were supposed to subtract 411\frac{4}{11} from a number, but accidentally added 411\frac{4}{11} and got 1011\frac{10}{11}. First recover the original number, then do the correct subtraction.
Fractions
Your answer
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: 1011\frac{10}{11} - 411\frac{4}{11} = 611\frac{6}{11}.

1011−411=611\frac{10}{11}-\frac{4}{11}=\frac{6}{11}
2STEP 2

Do the correct calculation

The correct operation subtracts 411\frac{4}{11} from the original number: 611\frac{6}{11} - 411\frac{4}{11} = 211\frac{2}{11}.

611−411=211\frac{6}{11}-\frac{4}{11}=\frac{2}{11}
Answer
211\frac{2}{11}
611−411=211\frac{6}{11}-\frac{4}{11}=\frac{2}{11}
Check: original 611\frac{6}{11} plus 411\frac{4}{11} really is 1011\frac{10}{11} (matches the mistake), and 611\frac{6}{11} minus 411\frac{4}{11} is 211\frac{2}{11}. The correct answer 211\frac{2}{11} is smaller than the wrong result 1011\frac{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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7 reasoning problems grow out of this type — the bridge toward competition →

▶ Practice — 10 problems