Compare Fractions: Find the Symbol Between 5/12 and 7/8

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

• Step 1: Identify the least common multiple (LCM) of the denominators 12 and 8.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Compare the converted fractions by examining their numerators.

Let's proceed with the solution:
Step 1: The LCM of 12 and 8 needs to be found. The factorization of 12 is $2^2 \times 3$ and for 8 is $2^3$. The LCM is $2^3 \times 3 = 24$. Therefore, the common denominator is 24.

Step 2: Convert each fraction to the new denominator:

• Convert $\frac{5}{12}$: The equivalent fraction is found by multiplying both the numerator and the denominator by a number that equals the common denominator when the original denominator is multiplied by it. $24 ÷ 12 = 2$. Thus, multiply both the numerator and denominator by 2: $\frac{5 \times 2}{12 \times 2} = \frac{10}{24}$.
• Convert $\frac{7}{8}$: Similarly, multiply by $24 ÷ 8 = 3$: $\frac{7 \times 3}{8 \times 3} = \frac{21}{24}$.

Step 3: Compare the two equivalent fractions $\frac{10}{24}$ and $\frac{21}{24}$. Comparing the numerators while the denominators are the same: 10 < 21.

Therefore, $\frac{5}{12}$ is less than $\frac{7}{8}$.

Thus, the correct sign to fill in is $<$.