Compare Fractions: Determine the Correct Sign Between 3/7 and 21/28

Fill in the missing sign:

$\frac{3}{7}☐\frac{21}{28}$

$<$To solve this problem, we must determine which relational operator (<, >, = ) should be placed between the fractions $\frac{3}{7}$ and $\frac{21}{28}$.

Step 1: Simplify $\frac{21}{28}$.

To simplify $\frac{21}{28}$, find the greatest common divisor (GCD) of 21 and 28. Factors of 21 are 1, 3, 7, 21, and factors of 28 are 1, 2, 4, 7, 14, 28. The GCD is 7.

Divide both the numerator and denominator of $\frac{21}{28}$ by 7:

$\frac{21}{28} = \frac{21 \div 7}{28 \div 7} = \frac{3}{4}$.

Now we compare $\frac{3}{7}$ and $\frac{3}{4}$.

Step 2: Convert both fractions to a common denominator for easy comparison. Use the least common multiple (LCM) of 7 and 4, which is 28.

- Convert $\frac{3}{7}$ to have a denominator of 28:

$\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}$.

- $\frac{3}{4}$ is already simplified and does not need to convert again, as we have considered LCM:

$\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}$.

Step 3: Compare the fractions $\frac{12}{28}$ and $\frac{21}{28}$.

- Since $\frac{12}{28} < \frac{21}{28}$, therefore, $\frac{3}{7} < \frac{21}{28}$.

Hence, the missing sign is $<$.