To find the fractions equivalent to \( \frac{15}{21} \), we can simplify \( \frac{15}{21} \) and compare it with the given fractions.
-
Simplifying \( \frac{15}{21} \):
- The greatest common divisor (GCD) of 15 and 21 is 3.
- Therefore, we can simplify \( \frac{15}{21} \) by dividing both the numerator and the denominator by 3: \[ \frac{15 \div 3}{21 \div 3} = \frac{5}{7} \]
-
Now, let's check each option:
- \( \frac{5}{7} \): This is equivalent since it's the simplified form of \( \frac{15}{21} \).
- \( \frac{30}{42} \): Check if it simplifies to \( \frac{5}{7} \):
- The GCD of 30 and 42 is 6.
- So, \( \frac{30 \div 6}{42 \div 6} = \frac{5}{7} \). This is equivalent.
- \( \frac{21}{15} \): This is not equivalent since it is simply the reciprocal of \( \frac{15}{21} \).
- \( \frac{25}{31} \): This does not reduce to \( \frac{5}{7} \) and is not equivalent.
- \( \frac{45}{84} \): Check if it simplifies to \( \frac{5}{7} \):
- The GCD of 45 and 84 is 9 (since 45 = 5 * 9 and 84 = 9 * 9.33).
- So, \( \frac{45 \div 9}{84 \div 9} = \frac{5}{9.33} \) (not exactly reducible), which is not equivalent to \( \frac{5}{7} \).
-
Equivalent fractions: Thus, the equivalent fractions to \( \frac{15}{21} \) are \( \frac{5}{7} \) and \( \frac{30}{42} \).
Final Answer: \( \frac{5}{7} \) and \( \frac{30}{42} \).
1 answer