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Dividing a whole number by a unit fraction worksheets

4 ÷ 1/3 asks how many thirds fit into 4, and the answer is 12. These free printable worksheets are the grade 5 step before dividing one fraction by another — the one that shows why dividing by a number smaller than one makes the answer bigger.

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Dividing a whole number by a unit fraction
Dividing a whole number by a unit fraction worksheet — Halves to eighths, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Each whole holds three thirds, so four wholes hold four lots of three: 4 ÷ 1/3 is 4 × 3. That is the whole method, and it is best reached by counting before any rule is named. Draw four bars, cut each into thirds and count the pieces, and 12 arrives without anyone mentioning multiplication — after which it is obvious why the denominator ends up multiplying the whole number.

Why this sheet works

The surprise is the size of the answer. Every question divides by a number less than one, so every answer is bigger than the number being divided: 5 ÷ 1/6 is 30. Children who have only ever divided whole numbers expect division to make things smaller, and an answer like 5/6 or 1/30 is the sign that the old expectation won. Every answer here is a whole number, so that slip shows at a glance.

How this one works

4 ÷

1 whole = 3 thirds
4 × 3 = 12
4 ÷ = 12
  1. 4 ÷ is asking a question: how many thirds fit inside 4?
  2. One whole cuts into 3 thirds. That is what the bottom number says.
  3. 4 wholes hold 4 lots of 3: 4 × 3 = 12.
  4. So 12 thirds fit inside 4. Dividing by a piece smaller than one gives MORE, not less.

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