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

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

5.NBT.B.7

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Generated variants — 10

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

Variant 1 easy

From a certain number you were supposed to subtract $1.25$ , but by mistake you added it instead, and got $5.83$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 1.25 from a number, but you accidentally added 1.25 instead and got 5.83. Find what the correct answer (the number minus 1.25) should be.

Givens

The mistaken calculation was number + 1.25 = 5.83.
The correct calculation should be number - 1.25.

Unknowns

The correct result, number - 1.25.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 1.25.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 1.25, so undo it by subtracting 1.25 from 5.83: 5.83 - 1.25 = 4.58. That is the original number.

5.83 - 1.25 = 4.58

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 1.25 from the original number as intended: 4.58 - 1.25 = 3.33.

4.58 - 1.25 = 3.33

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 3.33

4 · Reviewdoes it hold up?

Check: the original number 4.58 plus 1.25 is 5.83 (matches the mistake), and 4.58 minus 1.25 is 3.33. The correct answer 3.33 is smaller than the mistaken 5.83, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 1.25 = 2.5, so the correct answer is 5.83 - 2.5 = 3.33 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 5.83 - 1.25 and 4.58 - 1.25.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 2 easy

From a certain number you were supposed to subtract $1.9$ , but by mistake you added it instead, and got $6.05$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 1.9 from a number, but you accidentally added 1.9 instead and got 6.05. Find what the correct answer (the number minus 1.9) should be.

Givens

The mistaken calculation was number + 1.9 = 6.05.
The correct calculation should be number - 1.9.

Unknowns

The correct result, number - 1.9.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 1.9.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 1.9, so undo it by subtracting 1.9 from 6.05: 6.05 - 1.9 = 4.15. That is the original number.

6.05 - 1.9 = 4.15

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 1.9 from the original number as intended: 4.15 - 1.9 = 2.25.

4.15 - 1.9 = 2.25

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 2.25

4 · Reviewdoes it hold up?

Check: the original number 4.15 plus 1.9 is 6.05 (matches the mistake), and 4.15 minus 1.9 is 2.25. The correct answer 2.25 is smaller than the mistaken 6.05, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 1.9 = 3.8, so the correct answer is 6.05 - 3.8 = 2.25 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 6.05 - 1.9 and 4.15 - 1.9.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 3 easy

From a certain number you were supposed to subtract $2.5$ , but by mistake you added it instead, and got $8.42$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 2.5 from a number, but you accidentally added 2.5 instead and got 8.42. Find what the correct answer (the number minus 2.5) should be.

Givens

The mistaken calculation was number + 2.5 = 8.42.
The correct calculation should be number - 2.5.

Unknowns

The correct result, number - 2.5.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 2.5.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 2.5, so undo it by subtracting 2.5 from 8.42: 8.42 - 2.5 = 5.92. That is the original number.

8.42 - 2.5 = 5.92

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 2.5 from the original number as intended: 5.92 - 2.5 = 3.42.

5.92 - 2.5 = 3.42

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 3.42

4 · Reviewdoes it hold up?

Check: the original number 5.92 plus 2.5 is 8.42 (matches the mistake), and 5.92 minus 2.5 is 3.42. The correct answer 3.42 is smaller than the mistaken 8.42, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 2.5 = 5, so the correct answer is 8.42 - 5 = 3.42 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 8.42 - 2.5 and 5.92 - 2.5.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 4 medium

From a certain number you were supposed to subtract $3.15$ , but by mistake you added it instead, and got $9.74$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 3.15 from a number, but you accidentally added 3.15 instead and got 9.74. Find what the correct answer (the number minus 3.15) should be.

Givens

The mistaken calculation was number + 3.15 = 9.74.
The correct calculation should be number - 3.15.

Unknowns

The correct result, number - 3.15.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 3.15.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 3.15, so undo it by subtracting 3.15 from 9.74: 9.74 - 3.15 = 6.59. That is the original number.

9.74 - 3.15 = 6.59

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 3.15 from the original number as intended: 6.59 - 3.15 = 3.44.

6.59 - 3.15 = 3.44

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 3.44

4 · Reviewdoes it hold up?

Check: the original number 6.59 plus 3.15 is 9.74 (matches the mistake), and 6.59 minus 3.15 is 3.44. The correct answer 3.44 is smaller than the mistaken 9.74, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 3.15 = 6.3, so the correct answer is 9.74 - 6.3 = 3.44 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 9.74 - 3.15 and 6.59 - 3.15.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 5 medium

From a certain number you were supposed to subtract $4.04$ , but by mistake you added it instead, and got $10.98$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 4.04 from a number, but you accidentally added 4.04 instead and got 10.98. Find what the correct answer (the number minus 4.04) should be.

Givens

The mistaken calculation was number + 4.04 = 10.98.
The correct calculation should be number - 4.04.

Unknowns

The correct result, number - 4.04.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 4.04.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 4.04, so undo it by subtracting 4.04 from 10.98: 10.98 - 4.04 = 6.94. That is the original number.

10.98 - 4.04 = 6.94

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 4.04 from the original number as intended: 6.94 - 4.04 = 2.9.

6.94 - 4.04 = 2.9

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 2.9

4 · Reviewdoes it hold up?

Check: the original number 6.94 plus 4.04 is 10.98 (matches the mistake), and 6.94 minus 4.04 is 2.9. The correct answer 2.9 is smaller than the mistaken 10.98, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 4.04 = 8.08, so the correct answer is 10.98 - 8.08 = 2.9 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 10.98 - 4.04 and 6.94 - 4.04.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 6 medium

From a certain number you were supposed to subtract $4.8$ , but by mistake you added it instead, and got $11.63$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 4.8 from a number, but you accidentally added 4.8 instead and got 11.63. Find what the correct answer (the number minus 4.8) should be.

Givens

The mistaken calculation was number + 4.8 = 11.63.
The correct calculation should be number - 4.8.

Unknowns

The correct result, number - 4.8.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 4.8.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 4.8, so undo it by subtracting 4.8 from 11.63: 11.63 - 4.8 = 6.83. That is the original number.

11.63 - 4.8 = 6.83

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 4.8 from the original number as intended: 6.83 - 4.8 = 2.03.

6.83 - 4.8 = 2.03

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 2.03

4 · Reviewdoes it hold up?

Check: the original number 6.83 plus 4.8 is 11.63 (matches the mistake), and 6.83 minus 4.8 is 2.03. The correct answer 2.03 is smaller than the mistaken 11.63, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 4.8 = 9.6, so the correct answer is 11.63 - 9.6 = 2.03 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 11.63 - 4.8 and 6.83 - 4.8.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 7 medium

From a certain number you were supposed to subtract $5.6$ , but by mistake you added it instead, and got $14.37$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 5.6 from a number, but you accidentally added 5.6 instead and got 14.37. Find what the correct answer (the number minus 5.6) should be.

Givens

The mistaken calculation was number + 5.6 = 14.37.
The correct calculation should be number - 5.6.

Unknowns

The correct result, number - 5.6.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 5.6.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 5.6, so undo it by subtracting 5.6 from 14.37: 14.37 - 5.6 = 8.77. That is the original number.

14.37 - 5.6 = 8.77

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 5.6 from the original number as intended: 8.77 - 5.6 = 3.17.

8.77 - 5.6 = 3.17

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 3.17

4 · Reviewdoes it hold up?

Check: the original number 8.77 plus 5.6 is 14.37 (matches the mistake), and 8.77 minus 5.6 is 3.17. The correct answer 3.17 is smaller than the mistaken 14.37, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 5.6 = 11.2, so the correct answer is 14.37 - 11.2 = 3.17 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 14.37 - 5.6 and 8.77 - 5.6.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 8 hard

From a certain number you were supposed to subtract $6.7$ , but by mistake you added it instead, and got $15.29$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 6.7 from a number, but you accidentally added 6.7 instead and got 15.29. Find what the correct answer (the number minus 6.7) should be.

Givens

The mistaken calculation was number + 6.7 = 15.29.
The correct calculation should be number - 6.7.

Unknowns

The correct result, number - 6.7.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 6.7.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 6.7, so undo it by subtracting 6.7 from 15.29: 15.29 - 6.7 = 8.59. That is the original number.

15.29 - 6.7 = 8.59

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 6.7 from the original number as intended: 8.59 - 6.7 = 1.89.

8.59 - 6.7 = 1.89

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 1.89

4 · Reviewdoes it hold up?

Check: the original number 8.59 plus 6.7 is 15.29 (matches the mistake), and 8.59 minus 6.7 is 1.89. The correct answer 1.89 is smaller than the mistaken 15.29, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 6.7 = 13.4, so the correct answer is 15.29 - 13.4 = 1.89 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 15.29 - 6.7 and 8.59 - 6.7.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 9 hard

From a certain number you were supposed to subtract $7.2$ , but by mistake you added it instead, and got $18.56$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 7.2 from a number, but you accidentally added 7.2 instead and got 18.56. Find what the correct answer (the number minus 7.2) should be.

Givens

The mistaken calculation was number + 7.2 = 18.56.
The correct calculation should be number - 7.2.

Unknowns

The correct result, number - 7.2.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 7.2.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 7.2, so undo it by subtracting 7.2 from 18.56: 18.56 - 7.2 = 11.36. That is the original number.

18.56 - 7.2 = 11.36

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 7.2 from the original number as intended: 11.36 - 7.2 = 4.16.

11.36 - 7.2 = 4.16

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 4.16

4 · Reviewdoes it hold up?

Check: the original number 11.36 plus 7.2 is 18.56 (matches the mistake), and 11.36 minus 7.2 is 4.16. The correct answer 4.16 is smaller than the mistaken 18.56, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 7.2 = 14.4, so the correct answer is 18.56 - 14.4 = 4.16 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 18.56 - 7.2 and 11.36 - 7.2.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Variant 10 hard

From a certain number you were supposed to subtract $8.35$ , but by mistake you added it instead, and got $22.1$ . What is the result of calculating it correctly?

Your answer

Show solution

1 · Understandwhat's really being asked

You were supposed to subtract 8.35 from a number, but you accidentally added 8.35 instead and got 22.1. Find what the correct answer (the number minus 8.35) should be.

Givens

The mistaken calculation was number + 8.35 = 22.1.
The correct calculation should be number - 8.35.

Unknowns

The correct result, number - 8.35.

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 8.35.

3 · Execute2 carry out the plan

1Recover the original number

#11 Work Backwards 5.NBT.B.7

The wrong result came from adding 8.35, so undo it by subtracting 8.35 from 22.1: 22.1 - 8.35 = 13.75. That is the original number.

22.1 - 8.35 = 13.75

Undo a mistaken addition by subtracting the same amount.

2Do the correct calculation

#11 Work Backwards 5.NBT.B.7

Now subtract 8.35 from the original number as intended: 13.75 - 8.35 = 5.4.

13.75 - 8.35 = 5.4

With the real number found, just carry out the subtraction that was supposed to happen.

Answer: 5.4

4 · Reviewdoes it hold up?

Check: the original number 13.75 plus 8.35 is 22.1 (matches the mistake), and 13.75 minus 8.35 is 5.4. The correct answer 5.4 is smaller than the mistaken 22.1, which makes sense because subtracting gives less than adding.

Another way: Shortcut by Guess and Check on the gap: the wrong and right results differ by 2 x 8.35 = 16.7, so the correct answer is 22.1 - 16.7 = 5.4 - same value without finding the original number.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 22.1 - 8.35 and 13.75 - 8.35.

💡Takeaway. Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!

Where next?

← Back to the problem: Undo a wrong decimal operation to recover the start