Problem
Recover missing digits from column carries
A two-digit number with tens digit A and ones digit B is multiplied by 6, and the product is 288. We must find the digits A and B.
Base-ten numbersOperations
Your answer
Watch out In 48, the tens digit is the left digit and the ones digit is the right one — don't swap A and B.
How to solve
Strategy Work Backwards — The result of the multiplication is given, so we undo it: dividing 288 by 6 recovers the two-digit number, and reading its digits gives A and B. A quick column check confirms the carry.
1STEP 1
Undo the multiplication
Since the two-digit number times 6 equals 288, divide 288 by 6 to recover the number.
288 ÷ 6 = 48
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.
Why?
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.
Why?
Multiplying the hidden number by 6 stacks 6 equal copies of it, and that stack is exactly what makes 288.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
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.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Read off the digits
The recovered number is 48, so the tens digit A is 4 and the ones digit B is 8.
48 → A = 4, B = 8
Place value tells us the left digit is the tens and the right digit is the ones.
3.NBT.A.3Work Backwards3STEP 3
Check the column multiplication
Rebuild the product column by column to confirm 48 × 6 lands back on 288.
48 × 6 = 288
Rebuilding the product column by column confirms the carries line up exactly.
3.OA.B.5Guess And CheckAnswer
A = 4, B = 8
288 ÷ 6 = 48 → A = 4, B = 8
48 times 6 = 288 exactly, and both A=4 and B=8 are valid single digits with A not zero, so the two-digit number 48 is legitimate.
Takeaway
When you know the answer to a times problem, just divide to walk backwards to the hidden number, then read its digits!
- Undo the multiplication
- Read off the digits
- Check the column multiplication
Where next?
Level upsuggested
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Step back and solidifysuggested