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Divide a unit fraction by a whole number

Dividing a unit fraction 1/b1/b by a positive whole number nn means partitioning 1/b1/b into nn equal parts, so each part has value (1/b)÷n=1/(bn)(1/b)\div n=1/(bn). Fraction bars and number lines can show that the quotient is a smaller unit fraction and that multiplying it by nn restores 1/b1/b; the scope is limited to unit fractions and whole-number divisors, not arbitrary fraction division or advanced generalizations.

Detailed Explanation: Divide a unit fraction by a whole number

To divide a unit fraction by a whole number, split the unit fraction into that many equal parts.

For a unit fraction 1b\frac{1}{b} divided by nn:

1b÷n=1b⋅n\frac{1}{b}\div n=\frac{1}{b\cdot n}

Example: Find 14÷3\frac{1}{4}\div 3.

  1. Think of 14\frac{1}{4} as one of four equal parts of a whole.
  2. Split that 14\frac{1}{4} part into 33 equal pieces.
  3. The whole is now divided into 4⋅3=124\cdot 3=12 equal pieces, so each small piece is 112\frac{1}{12}.

Therefore,

14÷3=14⋅3=112\frac{1}{4}\div 3=\frac{1}{4\cdot 3}=\frac{1}{12}

You can check by multiplying the answer by 33:

3⋅112=312=143\cdot\frac{1}{12}=\frac{3}{12}=\frac{1}{4}

So, 112\frac{1}{12} is the correct answer.

Learn by doing: Divide a unit fraction by a whole number

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    Fraction Division - Simple by Whole - Don't Simplify

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