Compare Fractions: Find the Missing Symbol Between 4/6 and 3/4

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

• Step 1: Identify the given fractions $\frac{4}{6}$ and $\frac{3}{4}$.
• Step 2: Calculate the least common denominator (LCD) of 6 and 4.
• Step 3: Convert each fraction to have the common denominator and compare numerators.

Now, let's work through these steps:

Step 1: The given fractions are $\frac{4}{6}$ and $\frac{3}{4}$.

Step 2: Find the least common denominator of 6 and 4. The prime factorization of 6 is $2 \times 3$ and of 4 is $2^2$. The LCD is $2^2 \times 3 = 12$.

Step 3: Convert each fraction to this common denominator.

• Convert $\frac{4}{6}$ to have a denominator of 12: Multiply both numerator and denominator by 2 to get $\frac{4 \times 2}{6 \times 2} = \frac{8}{12}$.
• Convert $\frac{3}{4}$ to have a denominator of 12: Multiply both numerator and denominator by 3 to get $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.

Compare the numerators: 8 and 9. Since 8 is less than 9, we find that $\frac{4}{6} < \frac{3}{4}$.

Therefore, the correct sign to fill in is $<$, and the correct answer is:

$\frac{4}{6} < \frac{3}{4}$.