Lesson 12: Fractions as Partial Quotients (Optional)

Property

To model the division $a \div b$, you can partition $a$ wholes into $b$ equal shares.
The size of each share is the fraction $\frac{a}{b}$.

Examples

Property

The word quotient indicates division, which can be written as a fraction.
The phrase 'the quotient of $A$ and $B$' is translated into the algebraic expression $\frac{A}{B}$.
The dividend ($A$) becomes the numerator, and the divisor ($B$) becomes the denominator.

Examples

• The phrase 'the quotient of the sum of $a$ and $b$, and $c$' means you should first find the sum ($a+b$) and then divide by $c$. This is written as $\frac{a+b}{c}$.
• The phrase 'the quotient of $x$ and the difference of $y$ and 2' translates to the expression $\frac{x}{y-2}$.
• The phrase 'the quotient of the product of $5$ and $z$, and $w$' translates to the expression $\frac{5z}{w}$.

Explanation

When you read 'the quotient of' in a word problem, it's a signal to write a fraction. The first quantity mentioned after 'quotient of' goes on top (numerator), and the second quantity goes on the bottom (denominator).

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