Question

simply: (2 3/5 - 1 2/3)* 5/8

Answer 1

To simplify the expression \((2 \frac{3}{5} - 1 \frac{2}{3}) \times \frac{5}{8}\), we can follow these steps:

1. **Convert mixed numbers to improper fractions**:
- \(2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}\)
- \(1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}\)

2. **Subtract the fractions**:
- To subtract \(\frac{13}{5} - \frac{5}{3}\), we need a common denominator. The least common multiple of 5 and 3 is 15.
- Convert both fractions:
- \(\frac{13}{5} = \frac{13 \times 3}{5 \times 3} = \frac{39}{15}\)
- \(\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}\)
- Now subtract:
\[
\frac{39}{15} - \frac{25}{15} = \frac{39 - 25}{15} = \frac{14}{15}
\]

3. **Multiply by \(\frac{5}{8}\)**:
- Now we multiply \(\frac{14}{15}\) by \(\frac{5}{8}\):
\[
\frac{14}{15} \times \frac{5}{8} = \frac{14 \times 5}{15 \times 8} = \frac{70}{120}
\]

4. **Simplify the fraction**:
- The GCD of 70 and 120 is 10, so we can simplify:
\[
\frac{70 \div 10}{120 \div 10} = \frac{7}{12}
\]

Thus, the final simplified result is:
\[
\frac{7}{12}
\]