To address this question, let's convert each improper fraction to its corresponding mixed number.
1. Convert [tex]\( \frac{34}{3} \)[/tex] to a mixed number:
- First, divide the numerator by the denominator: [tex]\( 34 \div 3 = 11 \)[/tex] with a remainder of [tex]\( 1 \)[/tex].
- This means [tex]\( \frac{34}{3} \)[/tex] can be expressed as [tex]\( 11 \frac{1}{3} \)[/tex] (because [tex]\( 34 = 11 \times 3 + 1 \)[/tex]).
2. Convert [tex]\( \frac{79}{8} \)[/tex] to a mixed number:
- Divide the numerator by the denominator: [tex]\( 79 \div 8 = 9 \)[/tex] with a remainder of [tex]\( 7 \)[/tex].
- So, [tex]\( \frac{79}{8} \)[/tex] converts to [tex]\( 9 \frac{7}{8} \)[/tex] (because [tex]\( 79 = 9 \times 8 + 7 \)[/tex]).
3. Convert [tex]\( \frac{92}{11} \)[/tex] to a mixed number:
- Divide the numerator by the denominator: [tex]\( 92 \div 11 = 8 \)[/tex] with a remainder of [tex]\( 4 \)[/tex].
- Meaning [tex]\( \frac{92}{11} \)[/tex] is [tex]\( 8 \frac{4}{11} \)[/tex] (because [tex]\( 92 = 8 \times 11 + 4 \)[/tex]).
Now, we pair each improper fraction with its corresponding mixed number:
- [tex]\( \frac{34}{3} \)[/tex] → [tex]\( 11 \frac{1}{3} \)[/tex]
- [tex]\( \frac{79}{8} \)[/tex] → [tex]\( 9 \frac{7}{8} \)[/tex]
- [tex]\( \frac{92}{11} \)[/tex] → [tex]\( 8 \frac{4}{11} \)[/tex]
So, the final matched pairs are:
- [tex]\( \frac{34}{3} \)[/tex] matches with [tex]\( 11 \frac{1}{3} \)[/tex]
- [tex]\( \frac{79}{8} \)[/tex] matches with [tex]\( 9 \frac{7}{8} \)[/tex]
- [tex]\( \frac{92}{11} \)[/tex] matches with [tex]\( 8 \frac{4}{11} \)[/tex]
