Practice · Recover the original number from a wrong calculation · Sensim Math

Variant 1 easy

A number was supposed to have $1\frac{5}{6}$ subtracted from it, but by mistake $1\frac{5}{6}$ was added to it instead, giving $5\frac{3}{4}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $1\frac{5}{6}$ taken away. Instead it was added, and the result came to $5\frac{3}{4}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $1\frac{5}{6}$ .
It was added when it should have been subtracted.
The wrong answer was $5\frac{3}{4}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

1\frac{5}{6}

gave

5\frac{3}{4}

, so taking it back off returns the hidden number.

5\frac{3}{4} - 1\frac{5}{6}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 12 and subtract.

5\frac{3}{4} - 1\frac{5}{6} = 3\frac{11}{12}

The hidden number is

3\frac{11}{12}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

1\frac{5}{6}

off the hidden number, as was intended all along.

3\frac{11}{12} - 1\frac{5}{6} = 2\frac{1}{12}

The correct answer is

2\frac{1}{12}

.

Answer:

\frac{25}{12}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $5\frac{3}{4}$ - $2\frac{1}{12}$ should be 2 x $1\frac{5}{6}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $1\frac{5}{6}$ , so the answer is $5\frac{3}{4}$ - $3\frac{2}{3}$ = $2\frac{1}{12}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 2 easy

A number was supposed to have $2\frac{1}{3}$ subtracted from it, but by mistake $2\frac{1}{3}$ was added to it instead, giving $6\frac{1}{4}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $2\frac{1}{3}$ taken away. Instead it was added, and the result came to $6\frac{1}{4}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $2\frac{1}{3}$ .
It was added when it should have been subtracted.
The wrong answer was $6\frac{1}{4}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

2\frac{1}{3}

gave

6\frac{1}{4}

, so taking it back off returns the hidden number.

6\frac{1}{4} - 2\frac{1}{3}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 12 and subtract.

6\frac{1}{4} - 2\frac{1}{3} = 3\frac{11}{12}

The hidden number is

3\frac{11}{12}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

2\frac{1}{3}

off the hidden number, as was intended all along.

3\frac{11}{12} - 2\frac{1}{3} = 1\frac{7}{12}

The correct answer is

1\frac{7}{12}

.

Answer:

\frac{19}{12}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $6\frac{1}{4}$ - $1\frac{7}{12}$ should be 2 x $2\frac{1}{3}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $2\frac{1}{3}$ , so the answer is $6\frac{1}{4}$ - $4\frac{2}{3}$ = $1\frac{7}{12}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 3 easy

A number was supposed to have $3\frac{4}{5}$ subtracted from it, but by mistake $3\frac{4}{5}$ was added to it instead, giving $7\frac{5}{7}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $3\frac{4}{5}$ taken away. Instead it was added, and the result came to $7\frac{5}{7}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $3\frac{4}{5}$ .
It was added when it should have been subtracted.
The wrong answer was $7\frac{5}{7}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

3\frac{4}{5}

gave

7\frac{5}{7}

, so taking it back off returns the hidden number.

7\frac{5}{7} - 3\frac{4}{5}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 35 and subtract.

7\frac{5}{7} - 3\frac{4}{5} = 3\frac{32}{35}

The hidden number is

3\frac{32}{35}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

3\frac{4}{5}

off the hidden number, as was intended all along.

3\frac{32}{35} - 3\frac{4}{5} = \frac{4}{35}

The correct answer is

\frac{4}{35}

.

Answer:

\frac{4}{35}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $7\frac{5}{7}$ - $\frac{4}{35}$ should be 2 x $3\frac{4}{5}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $3\frac{4}{5}$ , so the answer is $7\frac{5}{7}$ - $7\frac{3}{5}$ = $\frac{4}{35}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 4 easy

A number was supposed to have $3\frac{1}{4}$ subtracted from it, but by mistake $3\frac{1}{4}$ was added to it instead, giving $8\frac{5}{6}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $3\frac{1}{4}$ taken away. Instead it was added, and the result came to $8\frac{5}{6}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $3\frac{1}{4}$ .
It was added when it should have been subtracted.
The wrong answer was $8\frac{5}{6}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

3\frac{1}{4}

gave

8\frac{5}{6}

, so taking it back off returns the hidden number.

8\frac{5}{6} - 3\frac{1}{4}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 12 and subtract.

8\frac{5}{6} - 3\frac{1}{4} = 5\frac{7}{12}

The hidden number is

5\frac{7}{12}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

3\frac{1}{4}

off the hidden number, as was intended all along.

5\frac{7}{12} - 3\frac{1}{4} = 2\frac{1}{3}

The correct answer is

2\frac{1}{3}

.

Answer:

\frac{7}{3}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $8\frac{5}{6}$ - $2\frac{1}{3}$ should be 2 x $3\frac{1}{4}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $3\frac{1}{4}$ , so the answer is $8\frac{5}{6}$ - $6\frac{1}{2}$ = $2\frac{1}{3}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 5 medium

A number was supposed to have $4\frac{3}{8}$ subtracted from it, but by mistake $4\frac{3}{8}$ was added to it instead, giving $9\frac{2}{5}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $4\frac{3}{8}$ taken away. Instead it was added, and the result came to $9\frac{2}{5}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $4\frac{3}{8}$ .
It was added when it should have been subtracted.
The wrong answer was $9\frac{2}{5}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

4\frac{3}{8}

gave

9\frac{2}{5}

, so taking it back off returns the hidden number.

9\frac{2}{5} - 4\frac{3}{8}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 40 and subtract.

9\frac{2}{5} - 4\frac{3}{8} = 5\frac{1}{40}

The hidden number is

5\frac{1}{40}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

4\frac{3}{8}

off the hidden number, as was intended all along.

5\frac{1}{40} - 4\frac{3}{8} = \frac{13}{20}

The correct answer is

\frac{13}{20}

.

Answer:

\frac{13}{20}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $9\frac{2}{5}$ - $\frac{13}{20}$ should be 2 x $4\frac{3}{8}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $4\frac{3}{8}$ , so the answer is $9\frac{2}{5}$ - $8\frac{3}{4}$ = $\frac{13}{20}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 6 medium

A number was supposed to have $1\frac{7}{9}$ subtracted from it, but by mistake $1\frac{7}{9}$ was added to it instead, giving $4\frac{1}{2}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $1\frac{7}{9}$ taken away. Instead it was added, and the result came to $4\frac{1}{2}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $1\frac{7}{9}$ .
It was added when it should have been subtracted.
The wrong answer was $4\frac{1}{2}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

1\frac{7}{9}

gave

4\frac{1}{2}

, so taking it back off returns the hidden number.

4\frac{1}{2} - 1\frac{7}{9}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 18 and subtract.

4\frac{1}{2} - 1\frac{7}{9} = 2\frac{13}{18}

The hidden number is

2\frac{13}{18}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

1\frac{7}{9}

off the hidden number, as was intended all along.

2\frac{13}{18} - 1\frac{7}{9} = \frac{17}{18}

The correct answer is

\frac{17}{18}

.

Answer:

\frac{17}{18}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $4\frac{1}{2}$ - $\frac{17}{18}$ should be 2 x $1\frac{7}{9}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $1\frac{7}{9}$ , so the answer is $4\frac{1}{2}$ - $3\frac{5}{9}$ = $\frac{17}{18}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 7 medium

A number was supposed to have $2\frac{3}{10}$ subtracted from it, but by mistake $2\frac{3}{10}$ was added to it instead, giving $7\frac{4}{9}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $2\frac{3}{10}$ taken away. Instead it was added, and the result came to $7\frac{4}{9}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $2\frac{3}{10}$ .
It was added when it should have been subtracted.
The wrong answer was $7\frac{4}{9}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

2\frac{3}{10}

gave

7\frac{4}{9}

, so taking it back off returns the hidden number.

7\frac{4}{9} - 2\frac{3}{10}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 90 and subtract.

7\frac{4}{9} - 2\frac{3}{10} = 5\frac{13}{90}

The hidden number is

5\frac{13}{90}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

2\frac{3}{10}

off the hidden number, as was intended all along.

5\frac{13}{90} - 2\frac{3}{10} = 2\frac{38}{45}

The correct answer is

2\frac{38}{45}

.

Answer:

\frac{128}{45}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $7\frac{4}{9}$ - $2\frac{38}{45}$ should be 2 x $2\frac{3}{10}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $2\frac{3}{10}$ , so the answer is $7\frac{4}{9}$ - $4\frac{3}{5}$ = $2\frac{38}{45}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 8 medium

A number was supposed to have $4\frac{1}{6}$ subtracted from it, but by mistake $4\frac{1}{6}$ was added to it instead, giving $10\frac{3}{8}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $4\frac{1}{6}$ taken away. Instead it was added, and the result came to $10\frac{3}{8}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $4\frac{1}{6}$ .
It was added when it should have been subtracted.
The wrong answer was $10\frac{3}{8}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

4\frac{1}{6}

gave

10\frac{3}{8}

, so taking it back off returns the hidden number.

10\frac{3}{8} - 4\frac{1}{6}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 24 and subtract.

10\frac{3}{8} - 4\frac{1}{6} = 6\frac{5}{24}

The hidden number is

6\frac{5}{24}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

4\frac{1}{6}

off the hidden number, as was intended all along.

6\frac{5}{24} - 4\frac{1}{6} = 2\frac{1}{24}

The correct answer is

2\frac{1}{24}

.

Answer:

\frac{49}{24}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $10\frac{3}{8}$ - $2\frac{1}{24}$ should be 2 x $4\frac{1}{6}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $4\frac{1}{6}$ , so the answer is $10\frac{3}{8}$ - $8\frac{1}{3}$ = $2\frac{1}{24}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 9 hard

A number was supposed to have $2\frac{5}{11}$ subtracted from it, but by mistake $2\frac{5}{11}$ was added to it instead, giving $6\frac{2}{3}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $2\frac{5}{11}$ taken away. Instead it was added, and the result came to $6\frac{2}{3}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $2\frac{5}{11}$ .
It was added when it should have been subtracted.
The wrong answer was $6\frac{2}{3}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

2\frac{5}{11}

gave

6\frac{2}{3}

, so taking it back off returns the hidden number.

6\frac{2}{3} - 2\frac{5}{11}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 33 and subtract.

6\frac{2}{3} - 2\frac{5}{11} = 4\frac{7}{33}

The hidden number is

4\frac{7}{33}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

2\frac{5}{11}

off the hidden number, as was intended all along.

4\frac{7}{33} - 2\frac{5}{11} = 1\frac{25}{33}

The correct answer is

1\frac{25}{33}

.

Answer:

\frac{58}{33}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $6\frac{2}{3}$ - $1\frac{25}{33}$ should be 2 x $2\frac{5}{11}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $2\frac{5}{11}$ , so the answer is $6\frac{2}{3}$ - $4\frac{10}{11}$ = $1\frac{25}{33}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 10 hard

A number was supposed to have $5\frac{2}{7}$ subtracted from it, but by mistake $5\frac{2}{7}$ was added to it instead, giving $12\frac{1}{3}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $5\frac{2}{7}$ taken away. Instead it was added, and the result came to $12\frac{1}{3}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $5\frac{2}{7}$ .
It was added when it should have been subtracted.
The wrong answer was $12\frac{1}{3}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

5\frac{2}{7}

gave

12\frac{1}{3}

, so taking it back off returns the hidden number.

12\frac{1}{3} - 5\frac{2}{7}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 21 and subtract.

12\frac{1}{3} - 5\frac{2}{7} = 7\frac{1}{21}

The hidden number is

7\frac{1}{21}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

5\frac{2}{7}

off the hidden number, as was intended all along.

7\frac{1}{21} - 5\frac{2}{7} = 1\frac{16}{21}

The correct answer is

1\frac{16}{21}

.

Answer:

\frac{37}{21}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $12\frac{1}{3}$ - $1\frac{16}{21}$ should be 2 x $5\frac{2}{7}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $5\frac{2}{7}$ , so the answer is $12\frac{1}{3}$ - $10\frac{4}{7}$ = $1\frac{16}{21}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 11 hard

A number was supposed to have $6\frac{5}{12}$ subtracted from it, but by mistake $6\frac{5}{12}$ was added to it instead, giving $14\frac{2}{7}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $6\frac{5}{12}$ taken away. Instead it was added, and the result came to $14\frac{2}{7}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $6\frac{5}{12}$ .
It was added when it should have been subtracted.
The wrong answer was $14\frac{2}{7}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

6\frac{5}{12}

gave

14\frac{2}{7}

, so taking it back off returns the hidden number.

14\frac{2}{7} - 6\frac{5}{12}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 84 and subtract.

14\frac{2}{7} - 6\frac{5}{12} = 7\frac{73}{84}

The hidden number is

7\frac{73}{84}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

6\frac{5}{12}

off the hidden number, as was intended all along.

7\frac{73}{84} - 6\frac{5}{12} = 1\frac{19}{42}

The correct answer is

1\frac{19}{42}

.

Answer:

\frac{61}{42}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $14\frac{2}{7}$ - $1\frac{19}{42}$ should be 2 x $6\frac{5}{12}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $6\frac{5}{12}$ , so the answer is $14\frac{2}{7}$ - $12\frac{5}{6}$ = $1\frac{19}{42}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Variant 12 hard

A number was supposed to have $7\frac{3}{5}$ subtracted from it, but by mistake $7\frac{3}{5}$ was added to it instead, giving $16\frac{1}{4}$ . Find the value of the correct calculation.

Your answer

Show solution

1 · Understandwhat's really being asked

A hidden number should have had $7\frac{3}{5}$ taken away. Instead it was added, and the result came to $16\frac{1}{4}$ . We need what the correct subtraction would have given.

Givens

The amount involved is $7\frac{3}{5}$ .
It was added when it should have been subtracted.
The wrong answer was $16\frac{1}{4}$ .

Unknowns

The value of the correct calculation.

Constraints

The hidden number is the same in both the wrong and the right calculation.

2 · Planchoose the strategy

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

The answer cannot be reached from the wrong result in one step. Undo the mistaken addition to recover the hidden number first, then do the subtraction that was meant.

3 · Execute3 carry out the plan

1Undo the mistaken addition

#11 Work Backwards 5.NF.A.2

Adding

7\frac{3}{5}

gave

16\frac{1}{4}

, so taking it back off returns the hidden number.

16\frac{1}{4} - 7\frac{3}{5}

Subtraction undoes the addition that should not have happened.

2Find the hidden number with a common denominator

#7 Identify Subproblems 5.NF.A.1

Put both over 20 and subtract.

16\frac{1}{4} - 7\frac{3}{5} = 8\frac{13}{20}

The hidden number is

8\frac{13}{20}

.

3Do the correct calculation (subtract)

#7 Identify Subproblems 5.NF.A.1

Now take

7\frac{3}{5}

off the hidden number, as was intended all along.

8\frac{13}{20} - 7\frac{3}{5} = 1\frac{1}{20}

The correct answer is

1\frac{1}{20}

.

Answer:

\frac{21}{20}

4 · Reviewdoes it hold up?

The wrong answer and the right one differ by twice the amount involved: $16\frac{1}{4}$ - $1\frac{1}{20}$ should be 2 x $7\frac{3}{5}$ , and it is.

Another way: Skip the hidden number entirely: subtracting instead of adding moves the result down by two lots of $7\frac{3}{5}$ , so the answer is $16\frac{1}{4}$ - $15\frac{1}{5}$ = $1\frac{1}{20}$ .

Standardsmin grade 5

5.NF.A.1 Add and subtract fractions with unlike denominators — Both subtractions, over unlike denominators.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions — Reading the mistake as an addition to be undone.

💡Takeaway. A wrong answer still holds the hidden number. Undo the mistake first, then do what was actually asked.

Recover the original number from a wrong calculation · 12 practice problems

Generated variants — 12

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