Which of the following fraction is the smallest ?

Options

A. `(13)/(16)`
B. `(17)/(21)`
C. `(15)/(19)`
D. `(7)/(8)`

Explanation

To determine which of the given fractions is the smallest, we can convert each fraction into its decimal form. The fractions provided are:

1. \( \frac{13}{16} \)
2. \( \frac{17}{21} \)
3. \( \frac{15}{19} \)
4. \( \frac{7}{8} \)

### Step 1: Convert \( \frac{13}{16} \) to decimal
To convert \( \frac{13}{16} \) to decimal, divide 13 by 16.

\[ 13 \div 16 = 0.8125 \]

### Step 2: Convert \( \frac{17}{21} \) to decimal
Next, divide 17 by 21.

\[ 17 \div 21 \approx 0.8095 \]

### Step 3: Convert \( \frac{15}{19} \) to decimal
Now, divide 15 by 19.

\[ 15 \div 19 \approx 0.7895 \]

### Step 4: Convert \( \frac{7}{8} \) to decimal
Finally, divide 7 by 8.

\[ 7 \div 8 = 0.875 \]

### Step 5: Compare the decimal values
Now we have the following decimal values:

- \( \frac{13}{16} = 0.8125 \)
- \( \frac{17}{21} \approx 0.8095 \)
- \( \frac{15}{19} \approx 0.7895 \)
- \( \frac{7}{8} = 0.875 \)

### Conclusion
Among these decimal values, \( 0.7895 \) (from \( \frac{15}{19} \)) is the smallest. Therefore, the smallest fraction is:

\[ \text{The smallest fraction is } \frac{15}{19}. \]