To convert an improper fraction to a mixed fraction, we follow these steps:
1. Divide the numerator by the denominator to find the whole number part of the mixed fraction.
2. Find the remainder of this division, which will be the numerator of the fractional part.
3. The denominator of the fractional part remains the same.
Let's do this for each of the given fractions:
### a) [tex]\(\frac{32}{5}\)[/tex]
1. Divide 32 by 5.
- 32 ÷ 5 = 6 (whole number part) with a remainder of 32 - (6 * 5) = 2.
2. Therefore, [tex]\(\frac{32}{5}\)[/tex] can be written as the mixed fraction:
[tex]\[
6 \frac{2}{5}
\][/tex]
### b) [tex]\(-\frac{27}{10}\)[/tex]
1. Divide -27 by 10.
- -27 ÷ 10 = -3 (whole number part) with a remainder of -27 - (-3 * 10) = 3.
2. Therefore, [tex]\(-\frac{27}{10}\)[/tex] can be written as the mixed fraction:
[tex]\[
-3 \frac{3}{10}
\][/tex]
### c) [tex]\(\frac{7}{3}\)[/tex]
1. Divide 7 by 3.
- 7 ÷ 3 = 2 (whole number part) with a remainder of 7 - (2 * 3) = 1.
2. Therefore, [tex]\(\frac{7}{3}\)[/tex] can be written as the mixed fraction:
[tex]\[
2 \frac{1}{3}
\][/tex]
Putting it all together, the mixed fractions are:
a) [tex]\(6 \frac{2}{5}\)[/tex]
b) [tex]\(-3 \frac{3}{10}\)[/tex]
c) [tex]\(2 \frac{1}{3}\)[/tex]
