Lesson 4: Generate Equivalent Fractions: Division

Property

To reduce a fraction, we rewrite it as an equivalent fraction with a smaller denominator.
To do this, we divide the numerator and the denominator by the same number.
For example, the fraction $\frac{4}{10}$ can be reduced to $\frac{2}{5}$ because both the numerator and denominator are divisible by 2.

Examples

• To reduce the fraction $\frac{9}{12}$, we can divide both the numerator and denominator by 3. This gives $\frac{9 \div 3}{12 \div 3} = \frac{3}{4}$.
• The fraction $\frac{10}{25}$ can be reduced by dividing the top and bottom by 5. This gives $\frac{10 \div 5}{25 \div 5} = \frac{2}{5}$.
• Let's reduce $\frac{24}{32}$. Both numbers are divisible by 8, so we get $\frac{24 \div 8}{32 \div 8} = \frac{3}{4}$.

Explanation

Reducing a fraction is like simplifying a picture. You group smaller pieces into larger, equal-sized ones. The total amount doesn't change, but the fraction becomes easier to understand and work with. It's all about finding the simplest form.

Property

To find all possible equivalent fractions for $\frac{a}{b}$ using division, identify all common factors of the numerator $a$ and the denominator $b$ that are greater than 1.
For each common factor $c$, a new equivalent fraction is found by calculating $\frac{a \div c}{b \div c}$.

Examples