Lesson 4: Relate Division and Multiplication

Property

To convert an improper fraction quotient $\frac{a}{b}$ to a mixed number, find the whole number quotient $q$ and remainder $r$ from the division $a \div b$. The mixed number is written as $q\frac{r}{b}$.

Examples

Property

By comparing the dividend ($a$) and the divisor ($b$), we can predict if the quotient will be greater than, less than, or equal to 1.

• If the dividend is larger than the divisor ($a > b$), the quotient is greater than 1: $\frac{a}{b} > 1$
• If the dividend is smaller than the divisor ($a < b$), the quotient is less than 1: $\frac{a}{b} < 1$
• If the dividend is equal to the divisor ($a = b$), the quotient is exactly 1: $\frac{a}{b} = 1$