← Undo a wrong fraction operation to recover the start · Work Backwards to Recover a Start Value

Undo a wrong fraction operation to recover the start · 10 practice problems

4.NF.B.3

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 27\frac{2}{7}

You were supposed to subtract 27\dfrac{2}{7} from a number, but by mistake you added it instead, and the result was 67\dfrac{6}{7}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 27\frac{2}{7} from a number, but accidentally added 27\frac{2}{7} and got 67\frac{6}{7}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 27\frac{2}{7}.
  • The mistaken operation: number plus 27\frac{2}{7}, which gave 67\frac{6}{7}.
  • All fractions have denominator 7.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 27\frac{2}{7}).
Constraints
  • Same denominator 7 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 27\frac{2}{7} to the number to get 67\frac{6}{7}. Undo it by subtracting 27\frac{2}{7}: original number = 67\frac{6}{7} - 27\frac{2}{7} = 47\frac{4}{7}.
67−27=47\dfrac{6}{7}-\dfrac{2}{7}=\dfrac{4}{7}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 27\frac{2}{7} from the original number: 47\frac{4}{7} - 27\frac{2}{7} = 27\frac{2}{7}.
47−27=27\dfrac{4}{7}-\dfrac{2}{7}=\dfrac{2}{7}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 27\frac{2}{7}
4 · Reviewdoes it hold up?

Check: original 47\frac{4}{7} plus 27\frac{2}{7} really is 67\frac{6}{7} (matches the mistake), and 47\frac{4}{7} minus 27\frac{2}{7} is 27\frac{2}{7}. The correct answer 27\frac{2}{7} is smaller than the wrong result 67\frac{6}{7}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 27\frac{2}{7} = 47\frac{4}{7}, so the correct answer = 67\frac{6}{7} - 47\frac{4}{7} = 27\frac{2}{7}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 7 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 2 easy answer: 29\frac{2}{9}

You were supposed to subtract 39\dfrac{3}{9} from a number, but by mistake you added it instead, and the result was 89\dfrac{8}{9}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 39\frac{3}{9} from a number, but accidentally added 39\frac{3}{9} and got 89\frac{8}{9}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 39\frac{3}{9}.
  • The mistaken operation: number plus 39\frac{3}{9}, which gave 89\frac{8}{9}.
  • All fractions have denominator 9.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 39\frac{3}{9}).
Constraints
  • Same denominator 9 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 39\frac{3}{9} to the number to get 89\frac{8}{9}. Undo it by subtracting 39\frac{3}{9}: original number = 89\frac{8}{9} - 39\frac{3}{9} = 59\frac{5}{9}.
89−39=59\dfrac{8}{9}-\dfrac{3}{9}=\dfrac{5}{9}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 39\frac{3}{9} from the original number: 59\frac{5}{9} - 39\frac{3}{9} = 29\frac{2}{9}.
59−39=29\dfrac{5}{9}-\dfrac{3}{9}=\dfrac{2}{9}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 29\frac{2}{9}
4 · Reviewdoes it hold up?

Check: original 59\frac{5}{9} plus 39\frac{3}{9} really is 89\frac{8}{9} (matches the mistake), and 59\frac{5}{9} minus 39\frac{3}{9} is 29\frac{2}{9}. The correct answer 29\frac{2}{9} is smaller than the wrong result 89\frac{8}{9}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 39\frac{3}{9} = 69\frac{6}{9}, so the correct answer = 89\frac{8}{9} - 69\frac{6}{9} = 29\frac{2}{9}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 9 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 3 easy answer: 310\frac{3}{10}

You were supposed to subtract 310\dfrac{3}{10} from a number, but by mistake you added it instead, and the result was 910\dfrac{9}{10}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 310\frac{3}{10} from a number, but accidentally added 310\frac{3}{10} and got 910\frac{9}{10}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 310\frac{3}{10}.
  • The mistaken operation: number plus 310\frac{3}{10}, which gave 910\frac{9}{10}.
  • All fractions have denominator 10.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 310\frac{3}{10}).
Constraints
  • Same denominator 10 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 310\frac{3}{10} to the number to get 910\frac{9}{10}. Undo it by subtracting 310\frac{3}{10}: original number = 910\frac{9}{10} - 310\frac{3}{10} = 610\frac{6}{10}.
910−310=610\dfrac{9}{10}-\dfrac{3}{10}=\dfrac{6}{10}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 310\frac{3}{10} from the original number: 610\frac{6}{10} - 310\frac{3}{10} = 310\frac{3}{10}.
610−310=310\dfrac{6}{10}-\dfrac{3}{10}=\dfrac{3}{10}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 310\frac{3}{10}
4 · Reviewdoes it hold up?

Check: original 610\frac{6}{10} plus 310\frac{3}{10} really is 910\frac{9}{10} (matches the mistake), and 610\frac{6}{10} minus 310\frac{3}{10} is 310\frac{3}{10}. The correct answer 310\frac{3}{10} is smaller than the wrong result 910\frac{9}{10}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 310\frac{3}{10} = 610\frac{6}{10}, so the correct answer = 910\frac{9}{10} - 610\frac{6}{10} = 310\frac{3}{10}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 10 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 4 medium answer: 211\frac{2}{11}

You were supposed to subtract 411\dfrac{4}{11} from a number, but by mistake you added it instead, and the result was 1011\dfrac{10}{11}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

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}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 411\frac{4}{11}.
  • The mistaken operation: number plus 411\frac{4}{11}, which gave 1011\frac{10}{11}.
  • All fractions have denominator 11.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 411\frac{4}{11}).
Constraints
  • Same denominator 11 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 411\frac{4}{11} to the number to get 1011\frac{10}{11}. Undo it by subtracting 411\frac{4}{11}: original number = 1011\frac{10}{11} - 411\frac{4}{11} = 611\frac{6}{11}.
1011−411=611\dfrac{10}{11}-\dfrac{4}{11}=\dfrac{6}{11}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
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\dfrac{6}{11}-\dfrac{4}{11}=\dfrac{2}{11}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 211\frac{2}{11}
4 · Reviewdoes it hold up?

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.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 411\frac{4}{11} = 811\frac{8}{11}, so the correct answer = 1011\frac{10}{11} - 811\frac{8}{11} = 211\frac{2}{11}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 11 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 5 medium answer: 312\frac{3}{12}

You were supposed to subtract 412\dfrac{4}{12} from a number, but by mistake you added it instead, and the result was 1112\dfrac{11}{12}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 412\frac{4}{12} from a number, but accidentally added 412\frac{4}{12} and got 1112\frac{11}{12}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 412\frac{4}{12}.
  • The mistaken operation: number plus 412\frac{4}{12}, which gave 1112\frac{11}{12}.
  • All fractions have denominator 12.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 412\frac{4}{12}).
Constraints
  • Same denominator 12 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 412\frac{4}{12} to the number to get 1112\frac{11}{12}. Undo it by subtracting 412\frac{4}{12}: original number = 1112\frac{11}{12} - 412\frac{4}{12} = 712\frac{7}{12}.
1112−412=712\dfrac{11}{12}-\dfrac{4}{12}=\dfrac{7}{12}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 412\frac{4}{12} from the original number: 712\frac{7}{12} - 412\frac{4}{12} = 312\frac{3}{12}.
712−412=312\dfrac{7}{12}-\dfrac{4}{12}=\dfrac{3}{12}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 312\frac{3}{12}
4 · Reviewdoes it hold up?

Check: original 712\frac{7}{12} plus 412\frac{4}{12} really is 1112\frac{11}{12} (matches the mistake), and 712\frac{7}{12} minus 412\frac{4}{12} is 312\frac{3}{12}. The correct answer 312\frac{3}{12} is smaller than the wrong result 1112\frac{11}{12}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 412\frac{4}{12} = 812\frac{8}{12}, so the correct answer = 1112\frac{11}{12} - 812\frac{8}{12} = 312\frac{3}{12}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 12 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 6 medium answer: 213\frac{2}{13}

You were supposed to subtract 513\dfrac{5}{13} from a number, but by mistake you added it instead, and the result was 1213\dfrac{12}{13}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 513\frac{5}{13} from a number, but accidentally added 513\frac{5}{13} and got 1213\frac{12}{13}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 513\frac{5}{13}.
  • The mistaken operation: number plus 513\frac{5}{13}, which gave 1213\frac{12}{13}.
  • All fractions have denominator 13.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 513\frac{5}{13}).
Constraints
  • Same denominator 13 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 513\frac{5}{13} to the number to get 1213\frac{12}{13}. Undo it by subtracting 513\frac{5}{13}: original number = 1213\frac{12}{13} - 513\frac{5}{13} = 713\frac{7}{13}.
1213−513=713\dfrac{12}{13}-\dfrac{5}{13}=\dfrac{7}{13}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 513\frac{5}{13} from the original number: 713\frac{7}{13} - 513\frac{5}{13} = 213\frac{2}{13}.
713−513=213\dfrac{7}{13}-\dfrac{5}{13}=\dfrac{2}{13}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 213\frac{2}{13}
4 · Reviewdoes it hold up?

Check: original 713\frac{7}{13} plus 513\frac{5}{13} really is 1213\frac{12}{13} (matches the mistake), and 713\frac{7}{13} minus 513\frac{5}{13} is 213\frac{2}{13}. The correct answer 213\frac{2}{13} is smaller than the wrong result 1213\frac{12}{13}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 513\frac{5}{13} = 1013\frac{10}{13}, so the correct answer = 1213\frac{12}{13} - 1013\frac{10}{13} = 213\frac{2}{13}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 13 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 7 medium answer: 314\frac{3}{14}

You were supposed to subtract 514\dfrac{5}{14} from a number, but by mistake you added it instead, and the result was 1314\dfrac{13}{14}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 514\frac{5}{14} from a number, but accidentally added 514\frac{5}{14} and got 1314\frac{13}{14}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 514\frac{5}{14}.
  • The mistaken operation: number plus 514\frac{5}{14}, which gave 1314\frac{13}{14}.
  • All fractions have denominator 14.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 514\frac{5}{14}).
Constraints
  • Same denominator 14 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 514\frac{5}{14} to the number to get 1314\frac{13}{14}. Undo it by subtracting 514\frac{5}{14}: original number = 1314\frac{13}{14} - 514\frac{5}{14} = 814\frac{8}{14}.
1314−514=814\dfrac{13}{14}-\dfrac{5}{14}=\dfrac{8}{14}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 514\frac{5}{14} from the original number: 814\frac{8}{14} - 514\frac{5}{14} = 314\frac{3}{14}.
814−514=314\dfrac{8}{14}-\dfrac{5}{14}=\dfrac{3}{14}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 314\frac{3}{14}
4 · Reviewdoes it hold up?

Check: original 814\frac{8}{14} plus 514\frac{5}{14} really is 1314\frac{13}{14} (matches the mistake), and 814\frac{8}{14} minus 514\frac{5}{14} is 314\frac{3}{14}. The correct answer 314\frac{3}{14} is smaller than the wrong result 1314\frac{13}{14}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 514\frac{5}{14} = 1014\frac{10}{14}, so the correct answer = 1314\frac{13}{14} - 1014\frac{10}{14} = 314\frac{3}{14}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 14 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 8 hard answer: 215\frac{2}{15}

You were supposed to subtract 615\dfrac{6}{15} from a number, but by mistake you added it instead, and the result was 1415\dfrac{14}{15}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 615\frac{6}{15} from a number, but accidentally added 615\frac{6}{15} and got 1415\frac{14}{15}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 615\frac{6}{15}.
  • The mistaken operation: number plus 615\frac{6}{15}, which gave 1415\frac{14}{15}.
  • All fractions have denominator 15.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 615\frac{6}{15}).
Constraints
  • Same denominator 15 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 615\frac{6}{15} to the number to get 1415\frac{14}{15}. Undo it by subtracting 615\frac{6}{15}: original number = 1415\frac{14}{15} - 615\frac{6}{15} = 815\frac{8}{15}.
1415−615=815\dfrac{14}{15}-\dfrac{6}{15}=\dfrac{8}{15}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 615\frac{6}{15} from the original number: 815\frac{8}{15} - 615\frac{6}{15} = 215\frac{2}{15}.
815−615=215\dfrac{8}{15}-\dfrac{6}{15}=\dfrac{2}{15}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 215\frac{2}{15}
4 · Reviewdoes it hold up?

Check: original 815\frac{8}{15} plus 615\frac{6}{15} really is 1415\frac{14}{15} (matches the mistake), and 815\frac{8}{15} minus 615\frac{6}{15} is 215\frac{2}{15}. The correct answer 215\frac{2}{15} is smaller than the wrong result 1415\frac{14}{15}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 615\frac{6}{15} = 1215\frac{12}{15}, so the correct answer = 1415\frac{14}{15} - 1215\frac{12}{15} = 215\frac{2}{15}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 15 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 9 hard answer: 217\frac{2}{17}

You were supposed to subtract 717\dfrac{7}{17} from a number, but by mistake you added it instead, and the result was 1617\dfrac{16}{17}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 717\frac{7}{17} from a number, but accidentally added 717\frac{7}{17} and got 1617\frac{16}{17}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 717\frac{7}{17}.
  • The mistaken operation: number plus 717\frac{7}{17}, which gave 1617\frac{16}{17}.
  • All fractions have denominator 17.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 717\frac{7}{17}).
Constraints
  • Same denominator 17 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 717\frac{7}{17} to the number to get 1617\frac{16}{17}. Undo it by subtracting 717\frac{7}{17}: original number = 1617\frac{16}{17} - 717\frac{7}{17} = 917\frac{9}{17}.
1617−717=917\dfrac{16}{17}-\dfrac{7}{17}=\dfrac{9}{17}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 717\frac{7}{17} from the original number: 917\frac{9}{17} - 717\frac{7}{17} = 217\frac{2}{17}.
917−717=217\dfrac{9}{17}-\dfrac{7}{17}=\dfrac{2}{17}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 217\frac{2}{17}
4 · Reviewdoes it hold up?

Check: original 917\frac{9}{17} plus 717\frac{7}{17} really is 1617\frac{16}{17} (matches the mistake), and 917\frac{9}{17} minus 717\frac{7}{17} is 217\frac{2}{17}. The correct answer 217\frac{2}{17} is smaller than the wrong result 1617\frac{16}{17}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 717\frac{7}{17} = 1417\frac{14}{17}, so the correct answer = 1617\frac{16}{17} - 1417\frac{14}{17} = 217\frac{2}{17}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 17 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 10 hard answer: 419\frac{4}{19}

You were supposed to subtract 719\dfrac{7}{19} from a number, but by mistake you added it instead, and the result was 1819\dfrac{18}{19}. Find the value you would get from the correct calculation.

Show solution
1 · Understandwhat's really being asked

You were supposed to subtract 719\frac{7}{19} from a number, but accidentally added 719\frac{7}{19} and got 1819\frac{18}{19}. I must first recover the original number, then do the correct subtraction.

Givens
  • The intended operation: number minus 719\frac{7}{19}.
  • The mistaken operation: number plus 719\frac{7}{19}, which gave 1819\frac{18}{19}.
  • All fractions have denominator 19.
Unknowns
  • The original number.
  • The result of the correct calculation (number minus 719\frac{7}{19}).
Constraints
  • Same denominator 19 throughout, so adding/subtracting just works on numerators.
2 · Planchoose the strategy

#11 Work Backwards · also uses: #7 Identify Subproblems

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.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 4.NF.B.3
The mistake added 719\frac{7}{19} to the number to get 1819\frac{18}{19}. Undo it by subtracting 719\frac{7}{19}: original number = 1819\frac{18}{19} - 719\frac{7}{19} = 1119\frac{11}{19}.
1819−719=1119\dfrac{18}{19}-\dfrac{7}{19}=\dfrac{11}{19}
Working backwards undoes the wrong step by doing its opposite.

2Do the correct calculation

#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 719\frac{7}{19} from the original number: 1119\frac{11}{19} - 719\frac{7}{19} = 419\frac{4}{19}.
1119−719=419\dfrac{11}{19}-\dfrac{7}{19}=\dfrac{4}{19}
With the real number found, the intended subtraction is a one-step like-denominator subtraction.
Answer: 419\frac{4}{19}
4 · Reviewdoes it hold up?

Check: original 1119\frac{11}{19} plus 719\frac{7}{19} really is 1819\frac{18}{19} (matches the mistake), and 1119\frac{11}{19} minus 719\frac{7}{19} is 419\frac{4}{19}. The correct answer 419\frac{4}{19} is smaller than the wrong result 1819\frac{18}{19}, which makes sense since subtracting should give less than adding.

Another way: Use the shortcut (tool 5): the wrong result is too big by 2 x 719\frac{7}{19} = 1419\frac{14}{19}, so the correct answer = 1819\frac{18}{19} - 1419\frac{14}{19} = 419\frac{4}{19}.

Standardsmin grade 4
  • 4.NF.B.3 Understand a fraction with numerator greater than one as sum of unit fractions — Subtracting like-denominator fractions over 19 to recover the number and compute the correct result.
💡Takeaway. This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!