Undo a wrong decimal operation to recover the start

5.NBT.B.7 · take · grade 5

Archetype: Work Backwards to Recover a Start Value · step in a 9-type progression

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?

Show solution

Understand

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.

Plan

#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.

Execute

#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.

#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

Review

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.

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 - 13.40 = 1.89 - same value without finding the original number.

Standards · min grade 5

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

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