The least among the fractions `(15)/(16) , (19)/(20) , (24)/(25) , (34)/(35)` is

Options

A. `(34)/(35)`
B. `(15)/(16)`
C. `(19)/(20)`
D. `(24)/(25)`

Answer

To find the least among the fractions \( \frac{15}{16}, \frac{19}{20}, \frac{24}{25}, \frac{34}{35} \), we can use cross multiplication to compare them step by step.

### Step 1: Compare \( \frac{15}{16} \) and \( \frac{19}{20} \)

To compare these two fractions, we perform cross multiplication:

\[ 15 \times 20 \quad \text{and} \quad 19 \times 16 \]

Calculating these:

\[ 15 \times 20 = 300 \]
\[ 19 \times 16 = 304 \]

Since \( 300 < 304 \), we have:

\[ \frac{15}{16} < \frac{19}{20} \]

### Step 2: Compare \( \frac{15}{16} \) and \( \frac{24}{25} \)

Next, we compare \( \frac{15}{16} \) with \( \frac{24}{25} \):

\[ 15 \times 25 \quad \text{and} \quad 16 \times 24 \]

Calculating these:

\[ 15 \times 25 = 375 \]
\[ 16 \times 24 = 384 \]

Since \( 375 < 384 \), we have:

\[ \frac{15}{16} < \frac{24}{25} \]

### Step 3: Compare \( \frac{15}{16} \) and \( \frac{34}{35} \)

Now, we compare \( \frac{15}{16} \) with \( \frac{34}{35} \):

\[ 15 \times 35 \quad \text{and} \quad 16 \times 34 \]

Calculating these:

\[ 15 \times 35 = 525 \]
\[ 16 \times 34 = 544 \]

Since \( 525 < 544 \), we have:

\[ \frac{15}{16} < \frac{34}{35} \]

### Conclusion

After comparing all fractions, we find that:

\[ \frac{15}{16} < \frac{19}{20}, \quad \frac{15}{16} < \frac{24}{25}, \quad \frac{15}{16} < \frac{34}{35} \]

Thus, the least among the fractions \( \frac{15}{16}, \frac{19}{20}, \frac{24}{25}, \frac{34}{35} \) is:

\[ \boxed{\frac{15}{16}} \]