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 No 25=410 512=1536 211=844

To determine if the fractions are equivalent, we can cross-multiply and see if the products are equal. Let's check each pair of fractions:

1. \(13 = \frac{5}{12}\)

   This means we're checking if \(13 \times 12 = 5\):

   • \(13 \times 12 = 156\)
   • \(5 \neq 156\)

   So, No, they are not equivalent.

2. \(25 = \frac{4}{10}\)

   This means we're checking if \(25 \times 10 = 4\):

   • \(25 \times 10 = 250\)
   • \(4 \neq 250\)

   So, No, they are not equivalent.

3. \( \frac{5}{12} = \frac{15}{36}\)

   This means we're checking if \(5 \times 36 = 15 \times 12\):

   • \(5 \times 36 = 180\)
   • \(15 \times 12 = 180\)

   So, Yes, they are equivalent.

   To find the number both the numerator and denominator were multiplied by: \[ \frac{5 \times 3}{12 \times 3} = \frac{15}{36} \] Here, both the numerator and denominator were multiplied by 3.

4. \( \frac{21}{84} = \frac{1}{4}\)

   This means we're checking if \(21 \times 4 = 1 \times 84\):

   • \(21 \times 4 = 84\)
   • \(1 \times 84 = 84\)

   So, Yes, they are equivalent.

   To find the number both the numerator and denominator were multiplied by: \[ \frac{1 \times 21}{4 \times 21} = \frac{21}{84} \] Here, both the numerator and denominator were multiplied by 21.

Summary:

• \(13 = \frac{5}{12}\): No
• \(25 = \frac{4}{10}\): No
• \( \frac{5}{12} = \frac{15}{36}\): Yes (multiplied by 3)
• \( \frac{21}{84} = \frac{1}{4}\): Yes (multiplied by 21)