Depth · one concept from first principles · step 2 of 4

Undo a wrong fraction operation to recover the start

You were supposed to subtract

\frac{4}{11}

from a number, but accidentally added

\frac{4}{11}

and got

\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: $\frac{10}{11}$ - $\frac{4}{11}$ = $\frac{6}{11}$ .

\frac{10}{11}-\frac{4}{11}=\frac{6}{11}

2STEP 2

Do the correct calculation

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

\frac{6}{11}-\frac{4}{11}=\frac{2}{11}

Answer

\frac{2}{11}

\frac{6}{11}-\frac{4}{11}=\frac{2}{11}

Check: original

\frac{6}{11}

plus

\frac{4}{11}

really is

\frac{10}{11}

(matches the mistake), and

\frac{6}{11}

minus

\frac{4}{11}

\frac{2}{11}

. The correct answer

\frac{2}{11}

is smaller than the wrong result

\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

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