Problem
Undo a wrong decimal operation to recover the start
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.
Base-ten numbers
Your answer
Watch out A common mistake is stopping once the original number is recovered and reporting 8.59 as the final answer, without doing the subtraction that was actually asked for.
How to solve
Strategy Work Backwards — First recover the original number by undoing the mistaken addition, then do the calculation correctly by subtracting 6.7.
1STEP 1
Recover the original number
Undo the mistaken addition 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.
5.NBT.B.7Work BackwardsSubtracting 6.7 from the mistaken result 15.29 gives back the original number, 8.59.
Why?
The wrong result 15.29 was made by adding 6.7 onto the original number, so taking that same 6.7 back off must leave the original number.
Why?
Subtraction takes away exactly the amount that addition piled on, so it reverses that earlier addition.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The subtraction 15.29 - 6.7 comes out to 8.59 by removing 6 ones and 7 tenths from the matching places of 15.29.
Why?
You can line the numbers up place under place and subtract each place on its own because every place holds ten of the place to its right.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
Do the correct calculation
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.
5.NBT.B.7Work BackwardsAnswer
1.89
8.59 - 6.7 = 1.89
Check: the original number 8.59 plus 6.7 is 15.29 (matches the mistake), and 8.59 minus 6.7 is 1.89, smaller than the mistaken 15.29 since subtracting gives less than adding.
Takeaway
Undo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!
- Recover the original number
- Do the correct calculation
Where next?
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