Answer
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Step 1:: Analyze the fractions given, which are 3 / 4 and 11 / 12.
To compare these fractions, we need to find the least common denominator (LCD) and determine if one fraction is greater than, less than, or equal to the other.
Step 2:: Find the least common multiple (LCM) of the denominators 4 and 12.
The prime factors of 4 are 2^2 and the prime factors of 12 are 2^2 * 3. The LCM is the product of the highest powers of all prime factors, so the LCM of 4 and 12 is 2^2 * 3 = 12.
Step 3:: To compare the fractions, we want to convert them to equivalent fractions with a common denominator of 12.
For 3 / 4, multiply both the numerator and denominator by 3 to get an equivalent fraction with a denominator of 12: (3 * 3) / (4 * 3) = 9 / 12.
Step 4:: For 11 / 12, the fraction is already in the desired form.
Step 5:: Compare the numerators of the equivalent fractions 9 / 12 and 11 / 12.
Since 11 is greater than 9, 11 / 12 is greater than 9 / 12, which is equivalent to 3 / 4.
Final Answer
\frac{3}{4} < \frac{11}{12}
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