Compare Fractions: Find the Missing Sign Between 3/8 and 1/9

To solve this problem, we'll follow these steps:

• Step 1: Calculate the least common denominator of the fractions
• Step 2: Convert both fractions to have this common denominator
• Step 3: Compare the numerators of the fractions with the common denominator
• Step 4: Select the appropriate inequality sign

Now, let's work through each step:

Step 1: The denominators of the given fractions are 8 and 9. The least common multiple (LCM) of these numbers is 72. Therefore, the least common denominator (LCD) is 72.

Step 2: Convert each fraction to an equivalent fraction with a denominator of 72.

• For $\frac{3}{8}$: Multiply the numerator and the denominator by 9 (since $\frac{72}{8} = 9$ ). This gives $\frac{3 \times 9}{8 \times 9} = \frac{27}{72}$.
• For $\frac{1}{9}$: Multiply the numerator and the denominator by 8 (since $\frac{72}{9} = 8$ ). This gives $\frac{1 \times 8}{9 \times 8} = \frac{8}{72}$.

Step 3: Now compare the numerators of $\frac{27}{72}$ and $\frac{8}{72}$.

Since $27$ is greater than $8$, it follows that $\frac{27}{72}$ is greater than $\frac{8}{72}$.

Step 4: Therefore, the correct inequality sign to fill the blank is $>$.

Thus, we conclude that $\frac{3}{8} > \frac{1}{9}$.

The correct answer is $\gt$.