1. The problem asks us to find equivalent fractions for $\frac{1}{4}$ and $\frac{1}{9}$ using the least common denominator. 2. To find equivalent fractions with the same denominator, we first find the least common denominator (LCD) of 4 and 9. 3. The denominators are 4 and 9. The prime factors are: - 4 = $2^2$ - 9 = $3^2$ 4. The LCD is the product of the highest powers of all prime factors: $$\text{LCD} = 2^2 \times 3^2 = 4 \times 9 = 36$$ 5. Now, convert each fraction to an equivalent fraction with denominator 36: - For $\frac{1}{4}$, multiply numerator and denominator by $\frac{36}{4} = 9$: $$\frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36}$$ - For $\frac{1}{9}$, multiply numerator and denominator by $\frac{36}{9} = 4$: $$\frac{1}{9} = \frac{1 \times 4}{9 \times 4} = \frac{4}{36}$$ 6. Therefore, the equivalent fractions are: $$\frac{1}{4} = \frac{9}{36}$$ $$\frac{1}{9} = \frac{4}{36}$$ These fractions have the least common denominator 36 and are equivalent to the original fractions.