Lesson 3: Use tape diagrams to model fractions as division.

Property

A division problem $a \div b$ can be modeled with a tape diagram.
The dividend, $a$, represents the total amount being shared.
The divisor, $b$, is the number of equal groups to divide the total into.
The size of one group is the quotient, which is the fraction $\frac{a}{b}$.

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 $5 \div 2 = 2\frac{1}{2}$.

Explanation

A tape diagram is a visual tool used to represent division. The total quantity being divided (the dividend) is drawn as a tape or a series of tapes. This total is then partitioned into a number of equal sections corresponding to the divisor. The size or value of one of these sections represents the quotient, showing how a division problem is equivalent to a fraction.