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R.1 Relate division and fractions

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What does it mean to relate division and fractions?

Division and fractions are closely connected. When you divide a number, you are finding out how many equal parts it can be split into. A fraction also shows equal parts of a whole. In fact, a fraction is another way to represent division.

Example:
  • 6 ÷ 2 can be written as 62
  • 6 ÷ 2 = 3, and the fraction 62 also equals 3
Note

Think of division and fractions as two ways to describe the same idea: sharing or grouping equally.

How can fractions show division?

A fraction shows how one number (the numerator) is divided by another number (the denominator). The numerator is the number being divided, and the denominator shows the number of equal parts.

Example:
  • 12 means 1 ÷ 2, or one whole divided into two equal parts.
  • 34 means 3 ÷ 4, or three wholes divided into four equal parts.
Note

Every fraction bar can be read as a division symbol. For example, 52 means “five divided by two.”

Using division to understand fractions

When you divide whole numbers that do not divide evenly, the answer can be expressed as a fraction. This helps show the exact value of a division problem.

Examples:
  • 7 ÷ 2 = 72 or 312
  • 5 ÷ 4 = 54 or 114
Note

If a division problem does not come out evenly, the remainder can be shown as a fraction to represent the part that is left over.

Visualizing division and fractions

Fractions and division can be represented with models or drawings. These help show how a whole is split into equal parts.

Example:
  • Dividing one pizza among four friends means each friend gets 14 of the pizza.
  • Dividing three pizzas among four friends means each friend gets 34 of a pizza.
Note

Visual models help you see that division and fractions describe equal sharing or equal parts of a whole.