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S.1 Divide unit fractions by whole numbers

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What does it mean to divide a unit fraction by a whole number?

A unit fraction is a fraction with a numerator of 1. When you divide a unit fraction by a whole number, you are splitting that fraction into smaller equal parts.

Example:
  • 13 ÷ 2 means you are dividing one-third into two equal parts.
  • Each part is 16.
Note

Dividing by a whole number makes the pieces smaller. The denominator becomes larger because you are creating more parts.

How do you divide a unit fraction by a whole number?

To divide a unit fraction by a whole number, multiply the denominator of the fraction by the whole number.

Steps:
  • Start with the unit fraction: 14
  • Divide by the whole number: 3
  • Multiply the denominator by 3: 4 × 3 = 12
  • The answer is 112.
Note

Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of that whole number.

Why does this work?

When you divide a unit fraction by a whole number, you are creating more equal parts of an already small piece. That makes each new piece smaller.

Example:
  • 12 ÷ 4 = 18
  • You started with one-half and divided it into four smaller parts. Each new part is one-eighth.
Note

This helps you understand that the larger the number you divide by, the smaller the result becomes.

Using division of unit fractions in real life

Dividing unit fractions can help solve real-world problems that involve sharing or dividing parts of a whole into smaller equal sections.

Example:
  • You have 13 of a pizza. You want to share it equally with 2 friends (3 people total).
  • You divide 13 by 3.
  • Each person gets 19 of the whole pizza.
Note

Word problems help you see how math connects to everyday life. Always check if your answer makes sense — smaller shares mean smaller fractions.