Which is greater between `(-4)/(9)` and `(-5)/(12)`?

Options

A. `(-4)/(9)`
B. `(-5)/(12)`
C. both are equal
D. can not compare

Answer

To determine which is greater between \(-\frac{4}{9}\) and \(-\frac{5}{12}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the fractions**: We have two fractions: \(-\frac{4}{9}\) and \(-\frac{5}{12}\).

2. **Find a common denominator**: The denominators are 9 and 12. We need to find the least common multiple (LCM) of these two numbers to compare the fractions easily.
- The multiples of 9 are: 9, 18, 27, 36, ...
- The multiples of 12 are: 12, 24, 36, ...
- The smallest common multiple is 36.

3. **Convert the fractions to have the same denominator**:
- For \(-\frac{4}{9}\):
\[ -\frac{4}{9} \times \frac{4}{4} = -\frac{16}{36} \]
- For \(-\frac{5}{12}\):
\[ -\frac{5}{12} \times \frac{3}{3} = -\frac{15}{36} \]

4. **Compare the new fractions**: Now we have:
- \(-\frac{16}{36}\) and \(-\frac{15}{36}\).
- Since both fractions have the same denominator, we can compare the numerators.

5. **Determine which is greater**:
- Compare the numerators: \(-16\) and \(-15\).
- In the number line, \(-16\) is to the left of \(-15\), which means \(-16\) is less than \(-15\).

6. **Conclusion**: Therefore, \(-\frac{5}{12}\) (which is \(-\frac{15}{36}\)) is greater than \(-\frac{4}{9}\) (which is \(-\frac{16}{36}\)).

### Final Answer:
\(-\frac{5}{12}\) is greater than \(-\frac{4}{9}\).

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