To approach and solve the given expression \(3 \frac{7}{9} - \frac{3}{5} + 1 \frac{3}{4} - 2 + \frac{1}{2}\), we need to follow a detailed, step-by-step process to ensure accuracy. Here's the breakdown:
1. Convert mixed numbers to improper fractions:
- For \(3 \frac{7}{9}\):
[tex]\[
3 \frac{7}{9} = 3 + \frac{7}{9}
\][/tex]
Convert the whole number to a fraction:
[tex]\[
3 = \frac{27}{9}
\][/tex]
So:
[tex]\[
3 + \frac{7}{9} = \frac{27}{9} + \frac{7}{9} = \frac{34}{9}
\][/tex]
- For \(1 \frac{3}{4}\):
[tex]\[
1 \frac{3}{4} = 1 + \frac{3}{4}
\][/tex]
Convert the whole number to a fraction:
[tex]\[
1 = \frac{4}{4}
\][/tex]
So:
[tex]\[
1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}
\][/tex]
2. Evaluate each fraction individually:
- \(3 \frac{7}{9} = \frac{34}{9} \approx 3.7778 \)
- \(\frac{3}{5} = 0.6\)
- \(1 \frac{3}{4} = \frac{7}{4} \approx 1.75\)
- \(2 = 2.0 \)
- \(\frac{1}{2} = 0.5\)
3. Perform addition and subtraction:
- Start with the first fraction: \(3.7778\).
- Subtract \(\frac{3}{5}(0.6) \):
[tex]\[
3.7778 - 0.6 = 3.1778
\][/tex]
- Add \(\frac{7}{4}(1.75) \):
[tex]\[
3.1778 + 1.75 = 4.9278
\][/tex]
- Subtract \(2\):
[tex]\[
4.9278 - 2 = 2.9278
\][/tex]
- Add \(\frac{1}{2}(0.5) \):
[tex]\[
2.9278 + 0.5 = 3.4278
\][/tex]
Therefore, the final result of the expression [tex]\(3 \frac{7}{9} - \frac{3}{5} + 1 \frac{3}{4} - 2 + \frac{1}{2}\)[/tex] is approximately [tex]\(3.4278\)[/tex].
