Arrange the fractions `(3)/(4),(5)/(12),(13)/(16),(16)/(29),(3)/(8)` in their descending order of magnitude.

Options

A. `(3)/(4) gt (3)/(8) gt (13)/(16) gt (16)/(29) gt (5)/(12)`
B. `(3)/(8) gt (5)/(12) gt (16)/(29) gt (3)/(4) gt (13)/(16)`
C. `(13)/(16) gt (3)/(4)gt (16)/(29) gt (5)/(12) gt (3)/(8)`
D. `(13)/(16) gt (16)/(29) gt (3)/(4) gt (5)/(12) gt (3)/(8)`

Answer

To arrange the fractions \( \frac{3}{4}, \frac{5}{12}, \frac{13}{16}, \frac{16}{29}, \frac{3}{8} \) in descending order, we will compare them step by step.

### Step 1: Find a common denominator
To compare the fractions easily, we can find a common denominator. The least common multiple (LCM) of the denominators \( 4, 12, 16, 29, \) and \( 8 \) is \( 464 \).

### Step 2: Convert each fraction to have the common denominator
Now we convert each fraction to have the denominator \( 464 \):

1. \( \frac{3}{4} = \frac{3 \times 116}{4 \times 116} = \frac{348}{464} \)
2. \( \frac{5}{12} = \frac{5 \times 39.333}{12 \times 39.333} = \frac{164.666}{464} \) (we can round this to \( \frac{165}{464} \) for simplicity)
3. \( \frac{13}{16} = \frac{13 \times 29}{16 \times 29} = \frac{377}{464} \)
4. \( \frac{16}{29} = \frac{16 \times 16}{29 \times 16} = \frac{256}{464} \)
5. \( \frac{3}{8} = \frac{3 \times 58}{8 \times 58} = \frac{174}{464} \)

### Step 3: List the converted fractions
Now we have the following fractions with a common denominator:

- \( \frac{3}{4} = \frac{348}{464} \)
- \( \frac{5}{12} = \frac{165}{464} \)
- \( \frac{13}{16} = \frac{377}{464} \)
- \( \frac{16}{29} = \frac{256}{464} \)
- \( \frac{3}{8} = \frac{174}{464} \)

### Step 4: Compare the numerators
Now we can compare the numerators:

- \( 348 \) (from \( \frac{3}{4} \))
- \( 165 \) (from \( \frac{5}{12} \))
- \( 377 \) (from \( \frac{13}{16} \))
- \( 256 \) (from \( \frac{16}{29} \))
- \( 174 \) (from \( \frac{3}{8} \))

### Step 5: Arrange in descending order
Now, we arrange the fractions based on the numerators in descending order:

1. \( \frac{13}{16} = \frac{377}{464} \) (largest)
2. \( \frac{3}{4} = \frac{348}{464} \)
3. \( \frac{3}{8} = \frac{174}{464} \)
4. \( \frac{16}{29} = \frac{256}{464} \)
5. \( \frac{5}{12} = \frac{165}{464} \) (smallest)

### Final Answer
The fractions in descending order are:
\[ \frac{13}{16}, \frac{3}{4}, \frac{3}{8}, \frac{16}{29}, \frac{5}{12} \]