Compare `(5)/(-12) and (-3)/(16)`.

Answer

To compare the rational numbers \( \frac{5}{-12} \) and \( \frac{-3}{16} \), we will follow these steps:

### Step 1: Identify the fractions
We have:
- \( \frac{5}{-12} \)
- \( \frac{-3}{16} \)

### Step 2: Convert to a common denominator
To compare these two fractions, we need to find a common denominator. The denominators are -12 and 16. The least common multiple (LCM) of 12 and 16 is 48.

### Step 3: Convert each fraction to have the common denominator
1. For \( \frac{5}{-12} \):
- To convert it to a denominator of 48, we multiply both the numerator and the denominator by 4:
\[ \frac{5}{-12} = \frac{5 \times 4}{-12 \times 4} = \frac{20}{-48} = \frac{-20}{48} \]

2. For \( \frac{-3}{16} \):
- To convert it to a denominator of 48, we multiply both the numerator and the denominator by 3:
\[ \frac{-3}{16} = \frac{-3 \times 3}{16 \times 3} = \frac{-9}{48} \]

### Step 4: Compare the two fractions
Now we have:
- \( \frac{-20}{48} \)
- \( \frac{-9}{48} \)

Since both fractions have the same denominator, we can compare the numerators:
- The numerator -20 is less than -9.

### Step 5: Conclusion
Since \( -20 < -9 \), we conclude that:
\[ \frac{5}{-12} < \frac{-3}{16} \]

Thus, \( \frac{5}{-12} \) is less than \( \frac{-3}{16} \).

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