Depth · one concept from first principles · step 2 of 4
In the multiplication below, find the digits and .
Here is the tens digit and is the ones digit of the two-digit number being multiplied. The two-digit number times equals .
Since the two-digit number times 6 equals 288, divide 288 by 6 to recover the number.
Multiplication and division are opposites, so dividing the product by 6 gives back the original number.
3.OA.A.3Work BackwardsDividing 288 by 6 gives back the original two-digit number that was multiplied by 6.
The number 288 was built by taking the hidden two-digit number 6 times, so pulling those 6 equal copies back apart returns that number.
Multiplying the hidden number by 6 stacks 6 equal copies of it, and that stack is exactly what makes 288.
Dividing 288 by 6 is the reverse move that unstacks those 6 equal copies, so it undoes the multiplication and lands on the original number.
The recovered number is 48, so the tens digit A is 4 and the ones digit B is 8.
Place value tells us the left digit is the tens and the right digit is the ones.
3.NBT.A.3Work BackwardsRebuild the product column by column to confirm 48 × 6 lands back on 288.
Rebuilding the product column by column confirms the carries line up exactly.
3.OA.B.5Guess And CheckWhen you know the answer to a times problem, just divide to walk backwards to the hidden number, then read its digits!
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