Practice · Undo a wrong fraction operation to recover the start · Sensim Math

Variant 1 easy

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{2}{7}$ .
The mistaken operation: number plus $\frac{2}{7}$ , which gave $\frac{6}{7}$ .
All fractions have denominator 7.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{2}{7}$ ).

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

\frac{2}{7}

to the number to get

\frac{6}{7}

. Undo it by subtracting

\frac{2}{7}

: original number =

\frac{6}{7}

-

\frac{2}{7}

=

\frac{4}{7}

.

\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

\frac{2}{7}

from the original number:

\frac{4}{7}

-

\frac{2}{7}

=

\frac{2}{7}

.

\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:

\frac{2}{7}

4 · Reviewdoes it hold up?

Check: original $\frac{4}{7}$ plus $\frac{2}{7}$ really is $\frac{6}{7}$ (matches the mistake), and $\frac{4}{7}$ minus $\frac{2}{7}$ is $\frac{2}{7}$ . The correct answer $\frac{2}{7}$ is smaller than the wrong result $\frac{6}{7}$ , 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 $\frac{2}{7}$ = $\frac{4}{7}$ , so the correct answer = $\frac{6}{7}$ - $\frac{4}{7}$ = $\frac{2}{7}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{3}{9}$ .
The mistaken operation: number plus $\frac{3}{9}$ , which gave $\frac{8}{9}$ .
All fractions have denominator 9.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{3}{9}$ ).

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

\frac{3}{9}

to the number to get

\frac{8}{9}

. Undo it by subtracting

\frac{3}{9}

: original number =

\frac{8}{9}

-

\frac{3}{9}

=

\frac{5}{9}

.

\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

\frac{3}{9}

from the original number:

\frac{5}{9}

-

\frac{3}{9}

=

\frac{2}{9}

.

\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:

\frac{2}{9}

4 · Reviewdoes it hold up?

Check: original $\frac{5}{9}$ plus $\frac{3}{9}$ really is $\frac{8}{9}$ (matches the mistake), and $\frac{5}{9}$ minus $\frac{3}{9}$ is $\frac{2}{9}$ . The correct answer $\frac{2}{9}$ is smaller than the wrong result $\frac{8}{9}$ , 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 $\frac{3}{9}$ = $\frac{6}{9}$ , so the correct answer = $\frac{8}{9}$ - $\frac{6}{9}$ = $\frac{2}{9}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{3}{10}$ .
The mistaken operation: number plus $\frac{3}{10}$ , which gave $\frac{9}{10}$ .
All fractions have denominator 10.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{3}{10}$ ).

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

\frac{3}{10}

to the number to get

\frac{9}{10}

. Undo it by subtracting

\frac{3}{10}

: original number =

\frac{9}{10}

-

\frac{3}{10}

=

\frac{6}{10}

.

\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

\frac{3}{10}

from the original number:

\frac{6}{10}

-

\frac{3}{10}

=

\frac{3}{10}

.

\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:

\frac{3}{10}

4 · Reviewdoes it hold up?

Check: original $\frac{6}{10}$ plus $\frac{3}{10}$ really is $\frac{9}{10}$ (matches the mistake), and $\frac{6}{10}$ minus $\frac{3}{10}$ is $\frac{3}{10}$ . The correct answer $\frac{3}{10}$ is smaller than the wrong result $\frac{9}{10}$ , 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 $\frac{3}{10}$ = $\frac{6}{10}$ , so the correct answer = $\frac{9}{10}$ - $\frac{6}{10}$ = $\frac{3}{10}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{4}{11}$ .
The mistaken operation: number plus $\frac{4}{11}$ , which gave $\frac{10}{11}$ .
All fractions have denominator 11.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{4}{11}$ ).

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

\frac{4}{11}

to the number to get

\frac{10}{11}

. Undo it by subtracting

\frac{4}{11}

: original number =

\frac{10}{11}

-

\frac{4}{11}

=

\frac{6}{11}

.

\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

\frac{4}{11}

from the original number:

\frac{6}{11}

-

\frac{4}{11}

=

\frac{2}{11}

.

\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:

\frac{2}{11}

4 · Reviewdoes it hold up?

Check: original $\frac{6}{11}$ plus $\frac{4}{11}$ really is $\frac{10}{11}$ (matches the mistake), and $\frac{6}{11}$ minus $\frac{4}{11}$ is $\frac{2}{11}$ . 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.

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

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{4}{12}$ .
The mistaken operation: number plus $\frac{4}{12}$ , which gave $\frac{11}{12}$ .
All fractions have denominator 12.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{4}{12}$ ).

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

\frac{4}{12}

to the number to get

\frac{11}{12}

. Undo it by subtracting

\frac{4}{12}

: original number =

\frac{11}{12}

-

\frac{4}{12}

=

\frac{7}{12}

.

\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

\frac{4}{12}

from the original number:

\frac{7}{12}

-

\frac{4}{12}

=

\frac{3}{12}

.

\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:

\frac{3}{12}

4 · Reviewdoes it hold up?

Check: original $\frac{7}{12}$ plus $\frac{4}{12}$ really is $\frac{11}{12}$ (matches the mistake), and $\frac{7}{12}$ minus $\frac{4}{12}$ is $\frac{3}{12}$ . The correct answer $\frac{3}{12}$ is smaller than the wrong result $\frac{11}{12}$ , 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 $\frac{4}{12}$ = $\frac{8}{12}$ , so the correct answer = $\frac{11}{12}$ - $\frac{8}{12}$ = $\frac{3}{12}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{5}{13}$ .
The mistaken operation: number plus $\frac{5}{13}$ , which gave $\frac{12}{13}$ .
All fractions have denominator 13.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{5}{13}$ ).

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

\frac{5}{13}

to the number to get

\frac{12}{13}

. Undo it by subtracting

\frac{5}{13}

: original number =

\frac{12}{13}

-

\frac{5}{13}

=

\frac{7}{13}

.

\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

\frac{5}{13}

from the original number:

\frac{7}{13}

-

\frac{5}{13}

=

\frac{2}{13}

.

\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:

\frac{2}{13}

4 · Reviewdoes it hold up?

Check: original $\frac{7}{13}$ plus $\frac{5}{13}$ really is $\frac{12}{13}$ (matches the mistake), and $\frac{7}{13}$ minus $\frac{5}{13}$ is $\frac{2}{13}$ . The correct answer $\frac{2}{13}$ is smaller than the wrong result $\frac{12}{13}$ , 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 $\frac{5}{13}$ = $\frac{10}{13}$ , so the correct answer = $\frac{12}{13}$ - $\frac{10}{13}$ = $\frac{2}{13}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{5}{14}$ .
The mistaken operation: number plus $\frac{5}{14}$ , which gave $\frac{13}{14}$ .
All fractions have denominator 14.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{5}{14}$ ).

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

\frac{5}{14}

to the number to get

\frac{13}{14}

. Undo it by subtracting

\frac{5}{14}

: original number =

\frac{13}{14}

-

\frac{5}{14}

=

\frac{8}{14}

.

\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

\frac{5}{14}

from the original number:

\frac{8}{14}

-

\frac{5}{14}

=

\frac{3}{14}

.

\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:

\frac{3}{14}

4 · Reviewdoes it hold up?

Check: original $\frac{8}{14}$ plus $\frac{5}{14}$ really is $\frac{13}{14}$ (matches the mistake), and $\frac{8}{14}$ minus $\frac{5}{14}$ is $\frac{3}{14}$ . The correct answer $\frac{3}{14}$ is smaller than the wrong result $\frac{13}{14}$ , 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 $\frac{5}{14}$ = $\frac{10}{14}$ , so the correct answer = $\frac{13}{14}$ - $\frac{10}{14}$ = $\frac{3}{14}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{6}{15}$ .
The mistaken operation: number plus $\frac{6}{15}$ , which gave $\frac{14}{15}$ .
All fractions have denominator 15.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{6}{15}$ ).

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

\frac{6}{15}

to the number to get

\frac{14}{15}

. Undo it by subtracting

\frac{6}{15}

: original number =

\frac{14}{15}

-

\frac{6}{15}

=

\frac{8}{15}

.

\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

\frac{6}{15}

from the original number:

\frac{8}{15}

-

\frac{6}{15}

=

\frac{2}{15}

.

\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:

\frac{2}{15}

4 · Reviewdoes it hold up?

Check: original $\frac{8}{15}$ plus $\frac{6}{15}$ really is $\frac{14}{15}$ (matches the mistake), and $\frac{8}{15}$ minus $\frac{6}{15}$ is $\frac{2}{15}$ . The correct answer $\frac{2}{15}$ is smaller than the wrong result $\frac{14}{15}$ , 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 $\frac{6}{15}$ = $\frac{12}{15}$ , so the correct answer = $\frac{14}{15}$ - $\frac{12}{15}$ = $\frac{2}{15}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{7}{17}$ .
The mistaken operation: number plus $\frac{7}{17}$ , which gave $\frac{16}{17}$ .
All fractions have denominator 17.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{7}{17}$ ).

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

\frac{7}{17}

to the number to get

\frac{16}{17}

. Undo it by subtracting

\frac{7}{17}

: original number =

\frac{16}{17}

-

\frac{7}{17}

=

\frac{9}{17}

.

\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

\frac{7}{17}

from the original number:

\frac{9}{17}

-

\frac{7}{17}

=

\frac{2}{17}

.

\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:

\frac{2}{17}

4 · Reviewdoes it hold up?

Check: original $\frac{9}{17}$ plus $\frac{7}{17}$ really is $\frac{16}{17}$ (matches the mistake), and $\frac{9}{17}$ minus $\frac{7}{17}$ is $\frac{2}{17}$ . The correct answer $\frac{2}{17}$ is smaller than the wrong result $\frac{16}{17}$ , 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 $\frac{7}{17}$ = $\frac{14}{17}$ , so the correct answer = $\frac{16}{17}$ - $\frac{14}{17}$ = $\frac{2}{17}$ .

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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

Givens

The intended operation: number minus $\frac{7}{19}$ .
The mistaken operation: number plus $\frac{7}{19}$ , which gave $\frac{18}{19}$ .
All fractions have denominator 19.

Unknowns

The original number.
The result of the correct calculation (number minus $\frac{7}{19}$ ).

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

\frac{7}{19}

to the number to get

\frac{18}{19}

. Undo it by subtracting

\frac{7}{19}

: original number =

\frac{18}{19}

-

\frac{7}{19}

=

\frac{11}{19}

.

\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

\frac{7}{19}

from the original number:

\frac{11}{19}

-

\frac{7}{19}

=

\frac{4}{19}

.

\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:

\frac{4}{19}

4 · Reviewdoes it hold up?

Check: original $\frac{11}{19}$ plus $\frac{7}{19}$ really is $\frac{18}{19}$ (matches the mistake), and $\frac{11}{19}$ minus $\frac{7}{19}$ is $\frac{4}{19}$ . The correct answer $\frac{4}{19}$ is smaller than the wrong result $\frac{18}{19}$ , 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 $\frac{7}{19}$ = $\frac{14}{19}$ , so the correct answer = $\frac{18}{19}$ - $\frac{14}{19}$ = $\frac{4}{19}$ .

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!

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

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