Out of fractions `3/7,2/9,4/13,5/11and7/9,`which is the second smallest fraction?

Options

A. `3/7, `
B. ` 2/9, `
C. `4/13,`
D. `,6/11`

Answer

To find the second smallest fraction among the given fractions \( \frac{3}{7}, \frac{2}{9}, \frac{4}{13}, \frac{5}{11}, \frac{7}{9} \), we will compare their values. Here’s a step-by-step solution:

### Step 1: Convert each fraction to decimal form
We will divide the numerator by the denominator for each fraction.

1. \( \frac{3}{7} \approx 0.4286 \)
2. \( \frac{2}{9} \approx 0.2222 \)
3. \( \frac{4}{13} \approx 0.3077 \)
4. \( \frac{5}{11} \approx 0.4545 \)
5. \( \frac{7}{9} \approx 0.7778 \)

### Step 2: List the decimal values
Now we list the decimal values we calculated:

- \( \frac{3}{7} \approx 0.4286 \)
- \( \frac{2}{9} \approx 0.2222 \)
- \( \frac{4}{13} \approx 0.3077 \)
- \( \frac{5}{11} \approx 0.4545 \)
- \( \frac{7}{9} \approx 0.7778 \)

### Step 3: Order the decimal values from smallest to largest
Next, we will arrange these decimal values in ascending order:

1. \( 0.2222 \) (which is \( \frac{2}{9} \))
2. \( 0.3077 \) (which is \( \frac{4}{13} \))
3. \( 0.4286 \) (which is \( \frac{3}{7} \))
4. \( 0.4545 \) (which is \( \frac{5}{11} \))
5. \( 0.7778 \) (which is \( \frac{7}{9} \))

### Step 4: Identify the second smallest fraction
From the ordered list, we can see that the smallest fraction is \( \frac{2}{9} \) and the second smallest fraction is \( \frac{4}{13} \).

### Final Answer
Thus, the second smallest fraction is \( \frac{4}{13} \).

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