Sure, let's convert these mixed numbers and improper fractions into improper fractions step-by-step.
### Mixed Number to Improper Fraction
1. Mixed Number: [tex]\(-3 \frac{2}{7}\)[/tex]
- We start with the whole number part, which is [tex]\(-3\)[/tex].
- Then, we have the fractional part, [tex]\(\frac{2}{7}\)[/tex].
To convert the mixed number [tex]\(-3 \frac{2}{7}\)[/tex] into an improper fraction, we follow these steps:
- Multiply the whole number part by the denominator of the fractional part: [tex]\(-3 \times 7 = -21\)[/tex].
- Add the numerator of the fractional part to this result: [tex]\(-21 + 2 = -19\)[/tex].
Now, we place this result over the original denominator:
[tex]\[
-3 \frac{2}{7} = \frac{-19}{7}
\][/tex]
Hence, the mixed number [tex]\(-3 \frac{2}{7}\)[/tex] is converted to the improper fraction [tex]\(\frac{-19}{7}\)[/tex], which is approximately [tex]\(-2.7142857142857144\)[/tex].
### Improper Fraction - No Conversion Needed
2. Improper Fraction: [tex]\(\frac{27}{5}\)[/tex]
- This is already an improper fraction, so there is no need for conversion.
The improper fraction [tex]\(\frac{27}{5}\)[/tex] is approximately [tex]\(5.4\)[/tex].
So, after conversion:
- The mixed number [tex]\(-3 \frac{2}{7}\)[/tex] converts to [tex]\(\frac{-19}{7}\)[/tex].
- The improper fraction [tex]\(\frac{27}{5}\)[/tex] remains as it is.
Thus, the converted values (in numerical approximation) are:
- [tex]\(\frac{-19}{7} \approx -2.7142857142857144\)[/tex]
- [tex]\(\frac{27}{5} \approx 5.4\)[/tex]
These results match exactly with our given numerical values confirming the conversions are correct.
