To solve the expression [tex]\(3 \frac{3}{5} + 1 \frac{2}{3} - 1 \frac{2}{5}\)[/tex], follow these steps:
1. Convert mixed fractions to improper fractions:
- For [tex]\(3 \frac{3}{5}\)[/tex]:
[tex]\[
3 \frac{3}{5} = \frac{3 \cdot 5 + 3}{5} = \frac{18}{5}
\][/tex]
- For [tex]\(1 \frac{2}{3}\)[/tex]:
[tex]\[
1 \frac{2}{3} = \frac{1 \cdot 3 + 2}{3} = \frac{5}{3}
\][/tex]
- For [tex]\(1 \frac{2}{5}\)[/tex]:
[tex]\[
1 \frac{2}{5} = \frac{1 \cdot 5 + 2}{5} = \frac{7}{5}
\][/tex]
2. Calculate the fractions in decimal form (for simplicity purposes in the following steps):
- [tex]\(\frac{18}{5} = 3.6\)[/tex]
- [tex]\(\frac{5}{3} \approx 1.6667\)[/tex]
- [tex]\(\frac{7}{5} = 1.4\)[/tex]
3. Add and subtract the fractions:
- First, add [tex]\(3.6\)[/tex] and [tex]\(1.6667\)[/tex]:
[tex]\[
3.6 + 1.6667 = 5.2667
\][/tex]
- Then, subtract [tex]\(1.4\)[/tex] from [tex]\(5.2667\)[/tex]:
[tex]\[
5.2667 - 1.4 = 3.8667
\][/tex]
Therefore, the result of [tex]\(3 \frac{3}{5} + 1 \frac{2}{3} - 1 \frac{2}{5}\)[/tex] is approximately [tex]\(3.8667\)[/tex].
