To convert the mixed number [tex]\(30 \frac{5}{7}\)[/tex] into an improper fraction, follow these steps:
1. Identify the whole number and the fraction part:
- Whole number: [tex]\(30\)[/tex]
- Fraction: [tex]\(\frac{5}{7}\)[/tex]
2. Convert the whole number to an equivalent fraction with the same denominator:
- [tex]\(30\)[/tex] as a fraction with the denominator [tex]\(7\)[/tex] is [tex]\(\frac{30 \cdot 7}{7} = \frac{210}{7}\)[/tex]
3. Add the fractions:
- Combine [tex]\(\frac{210}{7}\)[/tex] and [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
\frac{210}{7} + \frac{5}{7} = \frac{210 + 5}{7} = \frac{215}{7}
\][/tex]
Therefore, the mixed number [tex]\(30 \frac{5}{7}\)[/tex] as an improper fraction is [tex]\(\frac{215}{7}\)[/tex].
The correct answer is [tex]\(\frac{215}{7}\)[/tex].
