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← 4-2 · 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 answer: 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

Understand

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

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

Plan

#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.

Execute

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

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 3/10 = 6/10, so the correct answer = 9/10 - 6/10 = 3/10.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 2 answer: 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

Understand

You were supposed to subtract 4/11 from a number, but accidentally added 4/11 and got 10/11. I must first recover the original number, then do the correct subtraction.

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

Plan

#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.

Execute

#11 Work Backwards 4.NF.B.3
The mistake added 4/11 to the number to get 10/11. Undo it by subtracting 4/11: original number = 10/11 - 4/11 = 6/11.
1011−411=611\dfrac{10}{11}-\dfrac{4}{11}=\dfrac{6}{11}
Working backwards undoes the wrong step by doing its opposite.
#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 4/11 from the original number: 6/11 - 4/11 = 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: 2/11

Review

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.

Use the shortcut (tool 5): the wrong result is too big by 2 x 4/11 = 8/11, so the correct answer = 10/11 - 8/11 = 2/11.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 3 answer: 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

Understand

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

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

Plan

#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.

Execute

#11 Work Backwards 4.NF.B.3
The mistake added 3/9 to the number to get 8/9. Undo it by subtracting 3/9: original number = 8/9 - 3/9 = 5/9.
89−39=59\dfrac{8}{9}-\dfrac{3}{9}=\dfrac{5}{9}
Working backwards undoes the wrong step by doing its opposite.
#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 3/9 from the original number: 5/9 - 3/9 = 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: 2/9

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 3/9 = 6/9, so the correct answer = 8/9 - 6/9 = 2/9.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 4 answer: 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

Understand

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

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

Plan

#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.

Execute

#11 Work Backwards 4.NF.B.3
The mistake added 5/13 to the number to get 12/13. Undo it by subtracting 5/13: original number = 12/13 - 5/13 = 7/13.
1213−513=713\dfrac{12}{13}-\dfrac{5}{13}=\dfrac{7}{13}
Working backwards undoes the wrong step by doing its opposite.
#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 5/13 from the original number: 7/13 - 5/13 = 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: 2/13

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 5/13 = 10/13, so the correct answer = 12/13 - 10/13 = 2/13.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 5 answer: 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

Understand

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

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

Plan

#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.

Execute

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

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 2/7 = 4/7, so the correct answer = 6/7 - 4/7 = 2/7.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 6 answer: 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

Understand

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

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

Plan

#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.

Execute

#11 Work Backwards 4.NF.B.3
The mistake added 7/17 to the number to get 16/17. Undo it by subtracting 7/17: original number = 16/17 - 7/17 = 9/17.
1617−717=917\dfrac{16}{17}-\dfrac{7}{17}=\dfrac{9}{17}
Working backwards undoes the wrong step by doing its opposite.
#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 7/17 from the original number: 9/17 - 7/17 = 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: 2/17

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 7/17 = 14/17, so the correct answer = 16/17 - 14/17 = 2/17.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 7 answer: 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

Understand

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

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

Plan

#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.

Execute

#11 Work Backwards 4.NF.B.3
The mistake added 6/15 to the number to get 14/15. Undo it by subtracting 6/15: original number = 14/15 - 6/15 = 8/15.
1415−615=815\dfrac{14}{15}-\dfrac{6}{15}=\dfrac{8}{15}
Working backwards undoes the wrong step by doing its opposite.
#7 Identify Subproblems 4.NF.B.3
The correct operation subtracts 6/15 from the original number: 8/15 - 6/15 = 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: 2/15

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 6/15 = 12/15, so the correct answer = 14/15 - 12/15 = 2/15.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 8 answer: 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

Understand

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

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

Plan

#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.

Execute

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

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 7/19 = 14/19, so the correct answer = 18/19 - 14/19 = 4/19.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 9 answer: 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

Understand

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

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

Plan

#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.

Execute

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

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 4/12 = 8/12, so the correct answer = 11/12 - 8/12 = 3/12.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!
Variant 10 answer: 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

Understand

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

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

Plan

#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.

Execute

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

Review

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

Use the shortcut (tool 5): the wrong result is too big by 2 x 5/14 = 10/14, so the correct answer = 13/14 - 10/14 = 3/14.

Standards · min 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.
💡 This only needs Grade 4 fraction subtraction — work backwards to undo the mistake, then subtract the right way!