Grade 5 Math Puzzle 6: Use place-value structure

A free grade 5 math puzzle that teaches Use place-value structure. Try it first — the hint and the full solution open when you are ready.

Problem 6 · Use place-value structure · 4 points

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Nina's two-digit number becomes exactly 27 LARGER when its digits are reversed. What is the smallest number Nina could have written?

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Write the number as 10a + b. What is the reversed number worth?
Reversing changes the value by 9 × (difference of the digits).

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Answer: C — 14

A number 10a + b reversed becomes 10b + a; the change is 9(b − a). For +27 we need b − a = 3. The smallest such number takes a = 1, b = 4: the number 14 (41 − 14 = 27 ✓). Writing numbers by their place-value structure exposes exactly which digit relationships matter — pure abstract thinking about notation itself.

Grade 5 puzzle 6: Use place-value structure

Problem 6 · Use place-value structure · 4 points