To determine if the fractions are equivalent, we need to simplify the fractions and see if they result in the same value.
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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 \(5330 \neq 12800\), \(\frac{13}{25} \neq \frac{512}{410}\). -
For the second pair:
\(\frac{512}{410}\) and \(\frac{1536}{211}\)
Cross-multiply:
\(512 \times 211 = 108832\)
\(410 \times 1536 = 629760\)
Since \(108832 \neq 629760\), \(\frac{512}{410} \neq \frac{1536}{211}\). -
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.