Which of the following is in descending order?

Options

A. `3/8,8/15,11/23,26/81,`
B. `26/81,11/23,8/15,3/8`
C. `8/15,11/23,3/8,26/81`
D. `3/8,11/23,8/15,26/81`

Answer

To determine which of the given fractions is in descending order, we will follow these steps:

### Step 1: Identify the fractions
Let's assume the fractions given in the options are:
1. \( \frac{3}{8} \)
2. \( \frac{8}{15} \)
3. \( \frac{11}{23} \)
4. \( \frac{26}{81} \)

### Step 2: Find the LCM of the denominators
To compare these fractions, we need to convert them to have a common denominator. The denominators are 8, 15, 23, and 81. We will find the Least Common Multiple (LCM) of these numbers.

- The prime factorization of the denominators:
- \( 8 = 2^3 \)
- \( 15 = 3^1 \times 5^1 \)
- \( 23 = 23^1 \)
- \( 81 = 3^4 \)

The LCM will be:
\[ LCM = 2^3 \times 3^4 \times 5^1 \times 23^1 = 2^3 \times 81 \times 5 \times 23 \]
Calculating this gives us \( 2^3 = 8 \), \( 3^4 = 81 \), \( 5 = 5 \), and \( 23 = 23 \).

Calculating the LCM:
\[ LCM = 8 \times 81 \times 5 \times 23 = 2^3 \times 3^4 \times 5 \times 23 = 27720 \]

### Step 3: Convert each fraction to have the same denominator
Next, we will convert each fraction to have the denominator of 27720.

1. For \( \frac{3}{8} \):
\[ \frac{3}{8} = \frac{3 \times 3465}{8 \times 3465} = \frac{10395}{27720} \]

2. For \( \frac{8}{15} \):
\[ \frac{8}{15} = \frac{8 \times 1848}{15 \times 1848} = \frac{14784}{27720} \]

3. For \( \frac{11}{23} \):
\[ \frac{11}{23} = \frac{11 \times 1200}{23 \times 1200} = \frac{13200}{27720} \]

4. For \( \frac{26}{81} \):
\[ \frac{26}{81} = \frac{26 \times 344}{81 \times 344} = \frac{8944}{27720} \]

### Step 4: Compare the numerators
Now we have:
- \( \frac{10395}{27720} \)
- \( \frac{14784}{27720} \)
- \( \frac{13200}{27720} \)
- \( \frac{8944}{27720} \)

Now we can compare the numerators:
- \( 14784 > 13200 > 10395 > 8944 \)

### Step 5: Write the fractions in descending order
The fractions in descending order based on the numerators are:
1. \( \frac{8}{15} \)
2. \( \frac{11}{23} \)
3. \( \frac{3}{8} \)
4. \( \frac{26}{81} \)

### Final Answer
The descending order of the fractions is:
\[ \frac{8}{15}, \frac{11}{23}, \frac{3}{8}, \frac{26}{81} \]