Compare Fractions: Determine the Sign Between 3/8 and 1/4

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

• Step 1: Identify the denominators of the fractions $\frac{3}{8}$ and $\frac{1}{4}$.
• Step 2: Determine the least common denominator of 8 and 4.
• Step 3: Convert each fraction to have this common denominator.
• Step 4: Compare the fractions by examining their numerators.

Let's begin by determining the least common denominator (LCD) of the fractions:

The denominators are 8 and 4. The least common multiple (LCM) of these two numbers is 8.

Convert each fraction to an equivalent fraction with the common denominator of 8:

• $\frac{3}{8}$ already has the denominator 8, so it remains $\frac{3}{8}$.
• For $\frac{1}{4}$, convert by multiplying the numerator and denominator by 2:
$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$.

Now, compare these equivalent fractions: $\frac{3}{8}$ and $\frac{2}{8}$.

Since $3 > 2$, it follows that $\frac{3}{8} > \frac{2}{8}$.

Therefore, the correct sign for the missing space is $>$.

Thus, $\frac{3}{8} > \frac{1}{4}$.