To convert the mixed number [tex]\(-8 \frac{3}{8}\)[/tex] into an improper fraction, we can follow these steps:
1. Separate the whole number and the fractional part:
The mixed number [tex]\(-8 \frac{3}{8}\)[/tex] consists of the whole number part [tex]\(-8\)[/tex] and the fractional part [tex]\(\frac{3}{8}\)[/tex].
2. Convert the whole number to a fraction:
The whole number [tex]\(-8\)[/tex] can be written as a fraction with a denominator of 1:
[tex]\[
-8 = \frac{-8}{1}
\][/tex]
3. Express the whole number using the same denominator as the fractional part:
To combine the whole number fraction with the given fraction, both fractions need a common denominator. The common denominator here is 8. Convert [tex]\(\frac{-8}{1}\)[/tex] to a fraction with a denominator of 8:
[tex]\[
\frac{-8 \cdot 8}{1 \cdot 8} = \frac{-64}{8}
\][/tex]
4. Add the fractional part:
Now add the fractional part [tex]\(\frac{3}{8}\)[/tex] to the newly created fraction [tex]\(\frac{-64}{8}\)[/tex]:
[tex]\[
\frac{-64}{8} + \frac{3}{8}
\][/tex]
5. Combine the fractions:
Since both fractions have the same denominator, combine their numerators:
[tex]\[
\frac{-64 + 3}{8} = \frac{-61}{8}
\][/tex]
So, the mixed number [tex]\(-8 \frac{3}{8}\)[/tex] as an improper fraction is:
[tex]\[
\frac{-61}{8}
\][/tex]
