Compare Fractions: Finding the Missing Sign Between 3/7 and 1/8

To solve this problem, we will compare the fractions $\frac{3}{7}$ and $\frac{1}{8}$ by converting them to have a common denominator.

Step 1: Find the least common multiple (LCM) of the denominators 7 and 8. Since 7 and 8 are coprime (have no common factors other than 1), the LCM is simply the product of the two numbers:

$\text{LCM}(7, 8) = 7 \times 8 = 56$

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 56.

• Convert $\frac{3}{7}$:

• $\frac{3}{7} = \frac{3 \times 8}{7 \times 8} = \frac{24}{56}$

• Convert $\frac{1}{8}$:

• $\frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}$

Step 3: Compare the new numerators:

$\frac{24}{56} \quad \text{and} \quad \frac{7}{56}$

Since $24 > 7$, we conclude that $\frac{24}{56} > \frac{7}{56}$.

Therefore, the original inequality we are solving is:

$\frac{3}{7} > \frac{1}{8}$

Thus, the correct sign to fill in the blank is $\bm{>}$.