Sure! Let's convert each of the given improper fractions into mixed fractions. An improper fraction is where the numerator is greater than or equal to the denominator. To convert it to a mixed fraction, we can divide the numerator by the denominator to get the whole number part, and the remainder forms the fractional part.
### a) [tex]\(\frac{32}{5}\)[/tex]
1. Divide the numerator by the denominator to get the whole number part:
[tex]\[
\frac{32}{5} = 6 \text{ remainder } 2
\][/tex]
Here, [tex]\(32 \div 5 = 6\)[/tex] with a remainder of [tex]\(2\)[/tex].
2. Write the mixed fraction:
[tex]\[
6 \frac{2}{5}
\][/tex]
So, [tex]\(\frac{32}{5}\)[/tex] as a mixed fraction is [tex]\(6 \frac{2}{5}\)[/tex].
### b) [tex]\(-\frac{27}{10}\)[/tex]
1. Divide the numerator by the denominator to get the whole number part:
[tex]\[
\frac{-27}{10} = -3 \text{ remainder } 3
\][/tex]
Here, [tex]\(-27 \div 10 = -3\)[/tex] with a remainder of [tex]\(3\)[/tex].
2. Write the mixed fraction:
[tex]\[
-3 \frac{3}{10}
\][/tex]
Make sure to keep the negative sign in the whole number part.
So, [tex]\(-\frac{27}{10}\)[/tex] as a mixed fraction is [tex]\(-3 \frac{3}{10}\)[/tex].
### c) [tex]\(\frac{7}{3}\)[/tex]
1. Divide the numerator by the denominator to get the whole number part:
[tex]\[
\frac{7}{3} = 2 \text{ remainder } 1
\][/tex]
Here, [tex]\(7 \div 3 = 2\)[/tex] with a remainder of [tex]\(1\)[/tex].
2. Write the mixed fraction:
[tex]\[
2 \frac{1}{3}
\][/tex]
So, [tex]\(\frac{7}{3}\)[/tex] as a mixed fraction is [tex]\(2 \frac{1}{3}\)[/tex].
### Summary:
a) [tex]\(\frac{32}{5} = 6 \frac{2}{5}\)[/tex]
b) [tex]\(-\frac{27}{10} = -3 \frac{3}{10}\)[/tex]
c) [tex]\(\frac{7}{3} = 2 \frac{1}{3}\)[/tex]
