Depth · one concept from first principles · step 2 of 4
Undo the mistaken addition by subtracting 6.7 from 15.29: 15.29 - 6.7 = 8.59. That is the original number.
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.
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.
Subtraction takes away exactly the amount that addition piled on, so it reverses that earlier addition.
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.
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.
Now subtract 6.7 from the original number as intended: 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 BackwardsUndo the wrong move first - subtract back to the real number, then do the subtraction you were meant to do!
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Branching State Enumeration, Multiplicative Ratio with Integrality Constraints. Why the shapes repeat →