Simplifying Fractions:
To find an equivalent fraction, we can simplify the given fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

Finding the GCF:
To find the GCF of 12 and 27, we can list the factors of each number and find the greatest number that appears in both lists.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 27: 1, 3, 9, 27

The greatest number that appears in both lists is 3. Therefore, the GCF of 12 and 27 is 3.

Simplifying the Fraction:
To simplify the fraction 12/27, we divide both the numerator and denominator by the GCF.

12 ÷ 3 = 4
27 ÷ 3 = 9

So, the simplified form of 12/27 is 4/9.

Equivalent Fractions:
Equivalent fractions are fractions that represent the same value or amount. They have different numerators and denominators but are equal when simplified.

To check if the answer is correct, we can compare the simplified fraction 4/9 to the given options.

Option a) 2/9: This fraction is not equivalent to 4/9.

Option b) 3/9: This fraction is equivalent to 4/9 when further simplified. Since the question asks for an equivalent fraction, this could be a potential answer.

Option c) 4/9: This fraction is the simplified form of 12/27 and is equivalent.

Option d) 5/9: This fraction is not equivalent to 4/9.

Since option c) 4/9 is the simplified form of 12/27 and is equivalent, it is the correct answer.

Therefore, the correct answer is option c) 4/9.

Answer is c