Question

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

Answer 1

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**)