Lesson 3: Solve problems involving fraction division.

Property

To determine the correct division setup, identify what is being divided (the dividend) and what it is being divided by (the divisor).

• Finding the number of groups: When a total amount ($W$) is split into parts of a specific fractional size ($\frac{1}{d}$), the expression is $W \div \frac{1}{d}$.
• Finding the size of each group: When a fractional amount ($\frac{1}{d}$) is shared equally among a number of groups ($W$), the expression is $\frac{1}{d} \div W$.

Examples

Property

A tape diagram models fraction division by visually representing the dividend and the divisor.

1. Whole Number ÷ Unit Fraction ($a \div \frac{1}{b}$): Draw $a$ wholes and partition each whole into $b$ equal parts. The total number of parts is the quotient.
2. Unit Fraction ÷ Whole Number ($\frac{1}{b} \div a$): Draw one whole, represent the fraction $\frac{1}{b}$, and then partition that fractional part into $a$ equal pieces. The size of one new piece relative to the whole is the quotient.

Examples

Property

To solve word problems involving different units of measure, first convert one of the measurements so that all values share the same unit.
Then, perform the required fraction division.

Examples