Arrange in descending order:
a=4/10, b= 1/20, c=3/15, d= 6/5

Options

A. `b gt agt c gt d`
B. `d lt c lt a lt b`
C. `a lt c lt d lt b`
D. `d gt a gt c gt b`

Answer

To arrange the fractions \( a = \frac{4}{10}, b = \frac{1}{20}, c = \frac{3}{15}, d = \frac{6}{5} \) in descending order, we will follow these steps:

### Step 1: Convert all fractions to have a common denominator
To compare fractions easily, we can convert them to have a common denominator. The least common multiple (LCM) of the denominators (10, 20, 15, and 5) is 60.

- For \( a = \frac{4}{10} \):
\[ a = \frac{4 \times 6}{10 \times 6} = \frac{24}{60} \]

- For \( b = \frac{1}{20} \):
\[ b = \frac{1 \times 3}{20 \times 3} = \frac{3}{60} \]

- For \( c = \frac{3}{15} \):
\[ c = \frac{3 \times 4}{15 \times 4} = \frac{12}{60} \]

- For \( d = \frac{6}{5} \):
\[ d = \frac{6 \times 12}{5 \times 12} = \frac{72}{60} \]

### Step 2: Write the fractions with the common denominator
Now we have:
- \( a = \frac{24}{60} \)
- \( b = \frac{3}{60} \)
- \( c = \frac{12}{60} \)
- \( d = \frac{72}{60} \)

### Step 3: Compare the numerators
Now we can compare the numerators:
- \( 72 \) (from \( d \))
- \( 24 \) (from \( a \))
- \( 12 \) (from \( c \))
- \( 3 \) (from \( b \))

### Step 4: Arrange in descending order
From the comparison, we can arrange the fractions in descending order based on their numerators:
1. \( d = \frac{72}{60} \)
2. \( a = \frac{24}{60} \)
3. \( c = \frac{12}{60} \)
4. \( b = \frac{3}{60} \)

Thus, the descending order of the fractions is:
\[ d > a > c > b \]

### Final Answer:
The fractions in descending order are:
\[ d, a, c, b \quad \text{or} \quad \frac{6}{5}, \frac{4}{10}, \frac{3}{15}, \frac{1}{20} \]

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