Simplify Fractions D888B0

1. **State the problem:** Simplify the fractions $\frac{108}{16}$, $\frac{25}{100}$, and $\frac{81}{3}$. 2. **Recall the formula:** To simplify a fraction $\frac{a}{b}$, divide numerator and denominator by their greatest common factor (GCF). 3. **Simplify a. $\frac{108}{16}$:** - Find GCF of 108 and 16. - Prime factors: $108 = 2^2 \cdot 3^3$, $16 = 2^4$. - GCF is $2^2 = 4$. - Divide numerator and denominator by 4: $$\frac{108}{16} = \frac{\cancel{4} \cdot 27}{\cancel{4} \cdot 4} = \frac{27}{4}$$ 4. **Simplify b. $\frac{25}{100}$:** - Find GCF of 25 and 100. - Prime factors: $25 = 5^2$, $100 = 2^2 \cdot 5^2$. - GCF is $5^2 = 25$. - Divide numerator and denominator by 25: $$\frac{25}{100} = \frac{\cancel{25} \cdot 1}{\cancel{25} \cdot 4} = \frac{1}{4}$$ 5. **Simplify c. $\frac{81}{3}$:** - Find GCF of 81 and 3. - Prime factors: $81 = 3^4$, $3 = 3^1$. - GCF is $3$. - Divide numerator and denominator by 3: $$\frac{81}{3} = \frac{\cancel{3} \cdot 27}{\cancel{3} \cdot 1} = \frac{27}{1} = 27$$ **Final answers:** - a. $\frac{27}{4}$ - b. $\frac{1}{4}$ - c. $27$