Lesson 10: Fraction Division Situations

Property

Partitive division with a fraction dividend and whole number divisor, $\frac{a}{b} \div c$, answers the question: "If an amount $\frac{a}{b}$ is split into $c$ equal groups, what is the size of one group?"

Examples

Property

Quotative division, or measurement division, answers the question "how many groups of a certain size are in a given amount?" When dividing a whole number by a unit fraction, we are finding how many fractional pieces fit into the whole.

Examples

• How many $\frac{1}{4}$-cup servings are in 3 cups of sugar?

• A baker has 5 pounds of flour. How many $\frac{1}{2}$-pound bags can he make?

Explanation

This skill applies division to real-world scenarios where you need to find out how many smaller, fractional units can be made from a larger whole amount. This is known as quotative or measurement division. For example, if you are dividing 2 pies into slices that are $\frac{1}{6}$ of a pie each, you are asking how many groups of $\frac{1}{6}$ are in 2. Dividing a whole number by a unit fraction results in a larger whole number, as you are finding the total number of fractional parts within the wholes.