Which is the correct ascending order of the given numbers?

Options

A. `(17)/(24), (3)/(4) , (2)/(3)`
B. `(3)/(4) , (2)/(3) , (17)/(24)`
C. `(2)/(3) , (3)/(4) , (17)/(24)`
D. `(2)/(3) , (17)/(24) , (3)/(4)`

Answer

To determine the correct ascending order of the given fractions \( \frac{17}{24} \), \( \frac{3}{4} \), and \( \frac{2}{3} \), we can follow these steps:

### Step 1: Identify the fractions
We have three fractions:
1. \( \frac{17}{24} \)
2. \( \frac{3}{4} \)
3. \( \frac{2}{3} \)

### Step 2: Find a common denominator
To compare these fractions easily, we should convert them to have a common denominator. The denominators are 24, 4, and 3. The least common multiple (LCM) of these denominators is 24.

### Step 3: Convert each fraction to have the common denominator
- For \( \frac{17}{24} \), it already has the denominator of 24, so it remains \( \frac{17}{24} \).
- For \( \frac{3}{4} \), we need to convert it to a denominator of 24. We can do this by multiplying both the numerator and the denominator by 6:
\[ \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \]
- For \( \frac{2}{3} \), we convert it to a denominator of 24 by multiplying both the numerator and the denominator by 8:
\[ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \]

### Step 4: Compare the fractions
Now we have:
1. \( \frac{17}{24} \)
2. \( \frac{18}{24} \)
3. \( \frac{16}{24} \)

### Step 5: Arrange the fractions in ascending order
Now we can compare the numerators since the denominators are the same:
- \( 16 < 17 < 18 \)

Thus, the order from smallest to largest is:
1. \( \frac{16}{24} \) (which is \( \frac{2}{3} \))
2. \( \frac{17}{24} \)
3. \( \frac{18}{24} \) (which is \( \frac{3}{4} \))

### Final Answer
The correct ascending order of the given numbers is:
\[ \frac{2}{3}, \frac{17}{24}, \frac{3}{4} \]