Determine if the following pair of fractions is equivalent.

• A.
  Yes
• B. No
• C. Cannot be determined.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand that two fractions are equivalent if they represent the same value when simplified or converted to decimals.
2. Step 2: Simplify the first fraction \( \frac{9}{4} \) by checking if the numerator and denominator have any common factors. Since 9 and 4 share no common factors other than 1, \( \frac{9}{4} \) is already in simplest form.
3. Step 3: Simplify the second fraction \( \frac{27}{12} \) by finding the greatest common divisor (GCD) of 27 and 12, then divide both numerator and denominator by the GCD to get the fraction in simplest form.
4. Step 4: Compare the simplified forms of both fractions. If they are identical, the fractions are equivalent; if not, they are different.
5. Step 5: Alternatively, convert both fractions to decimal form by dividing numerator by denominator and compare the decimal values to check for equivalence.