Fill in the missing sign:
Fill in the missing sign:
< To solve this problem, we must determine which relational operator (<, >, = ) should be placed between the fractions and .
Step 1: Simplify .
To simplify , 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 by 7:
.
Now we compare and .
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 to have a denominator of 28:
.
- is already simplified and does not need to convert again, as we have considered LCM:
.
Step 3: Compare the fractions and .
- Since \frac{12}{28} < \frac{21}{28}, therefore, \frac{3}{7} < \frac{21}{28}.
Hence, the missing sign is < .
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