Lesson 2: Meanings of Fraction Division

Property

Division word problems can be categorized into two types based on the unknown information:

1. Group Size Unknown (Partitive Division): The total is divided into a known number of groups. The goal is to find the size of each group.

2. Number of Groups Unknown (Quotative Division): The total is divided by a known group size. The goal is to find the number of groups.

Property

To find an unknown number of groups, you can model division by starting with the total amount (dividend) and creating groups of a known size (divisor). The number of groups you make is the answer (quotient). This can be represented as:

Examples

Property

Dividing a whole number, $a$, by a unit fraction, $\frac{1}{b}$, is a way of asking: "How many groups of size $\frac{1}{b}$ are in $a$?"
This can be modeled visually to find the total number of fractional parts.

Examples

Property

To find the amount for a single share in an equal sharing situation (Partitive Division), divide the total amount by the number of shares. The result can be expressed as a fraction or a mixed number.

Examples

• To model $3 \div 4$, draw a tape diagram representing the whole number 3, and divide it into 4 equal parts. The value of one part is $\frac{3}{4}$.
• To model $5 \div 2$, draw 5 tape diagrams, each representing 1 whole. To share them into 2 equal groups, each group receives 2 whole tapes and $\frac{1}{2}$ of the last tape, showing that $5 \div 2 = 2\frac{1}{2}$.