Are the fractions equivalent? If so,what number were both the numerator and denominator multiplied by to arrive at the equivalent fraction?(4 points) 13=512 25=410 512=1536 211=844

To determine if the fractions are equivalent, we can simplify both sides of each equation and check if they yield the same value.

1. \( \frac{13}{25} \) and \( \frac{512}{410} \)

   • Simplifying \( \frac{512}{410} \): \[ \frac{512 \div 102.4}{410 \div 102.4} = \frac{5}{4} \]
   • \( \frac{13}{25} \) is in simplest form and cannot be simplified to \( \frac{5}{4} \).
   • These fractions are not equivalent.

2. \( \frac{512}{1536} \) and \( \frac{211}{844} \)

   • Simplifying \( \frac{512}{1536} \):
     • The GCD of 512 and 1536 is 512. \[ \frac{512 \div 512}{1536 \div 512} = \frac{1}{3} \]
   • Simplifying \( \frac{211}{844} \):
     • The GCD of 211 and 844 is 211. \[ \frac{211 \div 211}{844 \div 211} = \frac{1}{4} \]
   • \( \frac{1}{3} \) and \( \frac{1}{4} \) are not equal.
   • These fractions are not equivalent.

Therefore, based on the checks provided above, none of the presented pairs of fractions are equivalent.