To determine which pairs of numbers are equivalent, we need to analyze each pair individually.
### Pair 1: [tex]\(\frac{13}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex]
1. Convert the mixed number [tex]\(3 \frac{1}{4}\)[/tex] into an improper fraction:
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4}
\][/tex]
Calculate [tex]\(3\)[/tex] as [tex]\(\frac{3 \times 4}{4}\)[/tex]:
[tex]\[
3 = \frac{12}{4}
\][/tex]
Adding this to [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{12+1}{4} = \frac{13}{4}
\][/tex]
So the first pair [tex]\(\frac{13}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex] are indeed equivalent.
### Pair 2: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(0.25\)[/tex]
1. Convert [tex]\(\frac{2}{5}\)[/tex] into a decimal form:
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
2. Compare the decimal form with [tex]\(0.25\)[/tex]:
[tex]\[
0.4 \neq 0.25
\][/tex]
Therefore, [tex]\(\frac{2}{5}\)[/tex] and [tex]\(0.25\)[/tex] are not the same.
### Conclusion
Based on our analysis:
- [tex]\(\frac{13}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex] are equivalent.
- [tex]\(\frac{2}{5}\)[/tex] and [tex]\(0.25\)[/tex] are not equivalent.
So, the pair of equivalent numbers is [tex]\(\frac{13}{4}\)[/tex] and [tex]\(3 \frac{1}{4}\)[/tex].
