Compare Fractions: Determine if 1/5 is Greater or Less Than 3/4

To compare the fractions $\frac{1}{5}$ and $\frac{3}{4}$, we'll use the following steps:

• Step 1: Find a common denominator for the fractions.
• Step 2: Convert each fraction to an equivalent fraction with the common denominator.
• Step 3: Compare the numerators of the equivalent fractions.

Step 1: The denominators of the two fractions are 5 and 4. To find a common denominator, we multiply these together, getting $5 \times 4 = 20$. So, our common denominator is 20.

Step 2: Convert each fraction to have the denominator of 20.

• $\frac{1}{5}$: Multiply the numerator and denominator by 4 to get $\frac{1 \times 4}{5 \times 4} = \frac{4}{20}$.
• $\frac{3}{4}$: Multiply the numerator and denominator by 5 to get $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$.

Step 3: Now compare the numerators of the equivalent fractions:

$\frac{4}{20}$ compared to $\frac{15}{20}$ (both having the denominator of 20):

$4 < 15$ implies $\frac{4}{20} < \frac{15}{20}$.

Therefore, $\frac{1}{5} < \frac{3}{4}$.

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

Therefore, the missing sign in the expression $\frac{1}{5} ☐ \frac{3}{4}$ is $<$.