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 need to simplify the fractions and see if they result in the same value.

1. **For the first pair:**
\(\frac{13}{25}\) and \(\frac{512}{410}\)
To check if these fractions are equivalent, we can cross-multiply:
\(13 \times 410 = 5330\)
\(25 \times 512 = 12800\)
Since \(5330 \neq 12800\), \(\frac{13}{25} \neq \frac{512}{410}\).

2. **For the second pair:**
\(\frac{512}{410}\) and \(\frac{1536}{211}\)
Cross-multiply:
\(512 \times 211 = 108832\)
\(410 \times 1536 = 629760\)
Since \(108832 \neq 629760\), \(\frac{512}{410} \neq \frac{1536}{211}\).

3. **For the third pair:**
\(\frac{211}{844}\)
We can simplify \(\frac{211}{844}\):
Find the greatest common divisor (GCD) of 211 and 844, which is 211.
So, \(\frac{211 \div 211}{844 \div 211} = \frac{1}{4}\).

Now, we will check if that simplifies to one of the other valid fractions.

Also, check \(\frac{512}{410}\):
512 and 410 do not share a common factor easily, thus staying as is for now.

To conclude:
It appears that none of the fractions are equivalent.

**Final Answer:**
No, the fractions are not equivalent.