Final answer:
All options a) \(\frac{6}{10}\), b) \(\frac{9}{15}\), c) \(\frac{12}{20}\), and d) \(\frac{15}{25}\) provided are correct equivalent fractions for \(\frac{3}{5}\) since each results from multiplying both the numerator and denominator by a whole number.
Step-by-step explanation:
An equivalent fraction for \(\frac{3}{5}\) is a fraction that represents the same value when both the numerator (top number) and denominator (bottom number) are multiplied by the same factor. To find an equivalent fraction, you would multiply both 3 and 5 by the same whole number. Here are the options provided:
- Option a) \(\frac{6}{10}\): Multiplying both the numerator and denominator of \(\frac{3}{5}\) by 2 gives \(\frac{6}{10}\), which is equal to \(\frac{3}{5}\) because 6 is 3 times 2 and 10 is 5 times 2.
- Option b) \(\frac{9}{15}\): Multiplying both the numerator and denominator of \(\frac{3}{5}\) by 3 gives \(\frac{9}{15}\), which is equal to \(\frac{3}{5}\) because 9 is 3 times 3 and 15 is 5 times 3.
- Option c) \(\frac{12}{20}\): Multiplying both the numerator and denominator of \(\frac{3}{5}\) by 4 gives \(\frac{12}{20}\), which is equal to \(\frac{3}{5}\) because 12 is 3 times 4 and 20 is 5 times 4.
- Option d) \(\frac{15}{25}\): Multiplying both the numerator and denominator of \(\frac{3}{5}\) by 5 gives \(\frac{15}{25}\), which is equal to \(\frac{3}{5}\) because 15 is 3 times 5 and 25 is 5 times 5.
All options provided are equivalent fractions of \(\frac{3}{5}\). Therefore, the answer to the question could be any one of options a), b), c) or d).