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S.2 Divide whole numbers by unit fractions

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Divide whole numbers by unit fractions

Dividing a whole number by a unit fraction means finding how many parts of that fraction fit into the whole number. A unit fraction has a numerator of 1, such as 12 or 13.

Example:
  • 6 ÷ 12 = ?
  • Think: How many halves are in 6 wholes?
  • There are 12 halves in 6 wholes, so 6 ÷ 12 = 12.
Note

When you divide by a fraction, the answer is larger than the whole number because you are finding how many small parts fit inside the whole.

How to divide a whole number by a unit fraction

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

Steps:
  • Start with the problem: 4 ÷ 13
  • Keep the whole number (4) and multiply it by the denominator (3).
  • 4 × 3 = 12
  • So, 4 ÷ 13 = 12.
Note

You can remember this with the phrase: “To divide by a fraction, multiply by its denominator.”

Why does the answer get bigger?

When dividing by a unit fraction, you are asking how many small fractional parts fit into a whole. The smaller the fraction, the more of them fit inside one whole number—so the answer increases.

Example:
  • 8 ÷ 14 = 32
  • There are 4 quarters in 1 whole, so there are 8 × 4 = 32 quarters in 8 wholes.
Note

Smaller fractions make larger answers when dividing because you are counting more of them to make the whole.

Dividing whole numbers by unit fractions in real life

Understanding how to divide by unit fractions helps in solving real-world problems, like measuring, sharing, and cooking.

Example:
  • You have 5 cups of sugar, and each recipe uses 14 cup.
  • How many recipes can you make?
  • 5 ÷ 14 = 20 recipes.
Note

Dividing by unit fractions helps you find how many times a smaller part fits into a larger whole. It’s a useful skill in everyday situations.