Arrangement of fractions$\frac{1}{9}$,$\frac{1}{21}$,$\frac{3}{7}$,$\frac{12}{63}$ in decreasing order is :

Q: Arrangement of fractions$\frac{1}{9}$,$\frac{1}{21}$,$\frac{3}{7}$,$\frac{12}{63}$ in decreasing order is :

To determine the correct arrangement of the fractions $\frac{1}{9}$, $\frac{1}{21}$, $\frac{3}{7}$, and $\frac{12}{63}$ in decreasing order, we need to compare their values. 1. **Convert fractions to decimals for comparison:** - $\frac{1}{9} \approx 0.1111$ - $\frac{1}{21} \approx 0.0476$ - $\frac{3}{7} \approx 0.4286$ - $\frac{12}{63} = \frac{4}{21} \approx 0.1905$ 2. **Arrange the decimals in decreasing order:** - $0.4286$ (from $\frac{3}{7}$) - $0.1905$ (from $\frac{12}{63}$) - $0.1111$ (from $\frac{1}{9}$) - $0.0476$ (from $\frac{1}{21}$) 3. **Convert back to fractions:** - $\frac{3}{7}$, $\frac{12}{63}$, $\frac{1}{9}$, $\frac{1}{21}$ Thus, the correct arrangement in decreasing order is $\frac{3}{7}, \frac{12}{63}, \frac{1}{9}, \frac{1}{21}$, which corresponds to **Option 2**. **Explanation of why other options are incorrect:** - **Option 1: $\frac{3}{7}, \frac{1}{9}, \frac{12}{63}, \frac{1}{21}$** - This option incorrectly places $\frac{1}{9}$ before $\frac{12}{63}$. As shown in the decimal conversion, $\frac{12}{63}$ (0.1905) is greater than $\frac{1}{9}$ (0.1111). - **Option 3: $\frac{3}{7}, \frac{12}{63}, \(\frac{1}{21}, \frac{1}{9}$** - This option incorrectly places $\frac{1}{21}$ before $\frac{1}{9}$. As shown in the decimal conversion, $\frac{1}{9}$ (0.1111) is greater than $\frac{1}{21}$ (0.0476). - **Option 4: $\frac{1}{9}, \frac{12}{63}, \frac{3}{7}, \frac{1}{9}$** - This option incorrectly places $\frac{1}{9}$ at the beginning and repeats it, which is not the correct order based on their values. Therefore, Option 2 is the correct answer as it accurately reflects the decreasing order of the given fractions.

Question

Accepted Answer

To determine the correct arrangement of the fractions $\frac{1}{9}$, $\frac{1}{21}$, $\frac{3}{7}$, and $\frac{12}{63}$ in decreasing order, we need to compare their values.

1. **Convert fractions to decimals for comparison:**
   - $\frac{1}{9} \approx 0.1111$
   - $\frac{1}{21} \approx 0.0476$
   - $\frac{3}{7} \approx 0.4286$
   - $\frac{12}{63} = \frac{4}{21} \approx 0.1905$

2. **Arrange the decimals in decreasing order:**
   - $0.4286$ (from $\frac{3}{7}$)
   - $0.1905$ (from $\frac{12}{63}$)
   - $0.1111$ (from $\frac{1}{9}$)
   - $0.0476$ (from $\frac{1}{21}$)

3. **Convert back to fractions:**
   - $\frac{3}{7}$, $\frac{12}{63}$, $\frac{1}{9}$, $\frac{1}{21}$

Thus, the correct arrangement in decreasing order is $\frac{3}{7}, \frac{12}{63}, \frac{1}{9}, \frac{1}{21}$, which corresponds to **Option 2**.

**Explanation of why other options are incorrect:**

- **Option 1: $\frac{3}{7}, \frac{1}{9}, \frac{12}{63}, \frac{1}{21}$**
  - This option incorrectly places $\frac{1}{9}$ before $\frac{12}{63}$. As shown in the decimal conversion, $\frac{12}{63}$ (0.1905) is greater than $\frac{1}{9}$ (0.1111).

- **Option 3: $\frac{3}{7}, \frac{12}{63}, \(\frac{1}{21}, \frac{1}{9}$**
  - This option incorrectly places $\frac{1}{21}$ before $\frac{1}{9}$. As shown in the decimal conversion, $\frac{1}{9}$ (0.1111) is greater than $\frac{1}{21}$ (0.0476).

- **Option 4: $\frac{1}{9}, \frac{12}{63}, \frac{3}{7}, \frac{1}{9}$**
  - This option incorrectly places $\frac{1}{9}$ at the beginning and repeats it, which is not the correct order based on their values.

Therefore, Option 2 is the correct answer as it accurately reflects the decreasing order of the given fractions.