Write the following fractions in ascending order:
`3/(5), 4/(7), 2/(3), 3/(4), 9/(5)`

Answer

To write the fractions \( \frac{3}{5}, \frac{4}{7}, \frac{2}{3}, \frac{3}{4}, \frac{9}{5} \) in ascending order, we can follow these steps:

### Step 1: Convert each fraction to a decimal
1. **Convert \( \frac{3}{5} \)**:
\[ \frac{3}{5} = 0.6 \]

2. **Convert \( \frac{4}{7} \)**:
\[ \frac{4}{7} \approx 0.5714 \quad (\text{using long division or a calculator}) \]

3. **Convert \( \frac{2}{3} \)**:
\[ \frac{2}{3} \approx 0.6667 \quad (\text{using long division or a calculator}) \]

4. **Convert \( \frac{3}{4} \)**:
\[ \frac{3}{4} = 0.75 \]

5. **Convert \( \frac{9}{5} \)**:
\[ \frac{9}{5} = 1.8 \]

### Step 2: List the decimal equivalents
Now we have the following decimal equivalents:
- \( \frac{3}{5} = 0.6 \)
- \( \frac{4}{7} \approx 0.5714 \)
- \( \frac{2}{3} \approx 0.6667 \)
- \( \frac{3}{4} = 0.75 \)
- \( \frac{9}{5} = 1.8 \)

### Step 3: Arrange the decimals in ascending order
Now we will arrange the decimals from smallest to largest:
1. \( 0.5714 \) (which is \( \frac{4}{7} \))
2. \( 0.6 \) (which is \( \frac{3}{5} \))
3. \( 0.6667 \) (which is \( \frac{2}{3} \))
4. \( 0.75 \) (which is \( \frac{3}{4} \))
5. \( 1.8 \) (which is \( \frac{9}{5} \))

### Step 4: Write the fractions in ascending order
Thus, the fractions in ascending order are:
\[ \frac{4}{7}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{9}{5} \]