Which is larger out of `(2)/(3)` and `(-4)/(5)`?

Answer

To determine which is larger between \( \frac{2}{3} \) and \( \frac{-4}{5} \), we can follow these steps:

### Step 1: Identify the two fractions
We have two fractions to compare:
- \( \frac{2}{3} \)
- \( \frac{-4}{5} \)

### Step 2: Convert both fractions to have a common denominator
To compare the two fractions easily, we can convert them to have a common denominator. The denominators are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15.

### Step 3: Convert \( \frac{2}{3} \) to a fraction with a denominator of 15
We can convert \( \frac{2}{3} \) as follows:
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

### Step 4: Convert \( \frac{-4}{5} \) to a fraction with a denominator of 15
Now, we convert \( \frac{-4}{5} \):
\[ \frac{-4}{5} = \frac{-4 \times 3}{5 \times 3} = \frac{-12}{15} \]

### Step 5: Compare the two fractions
Now we have:
- \( \frac{10}{15} \)
- \( \frac{-12}{15} \)

Since \( 10 \) is greater than \( -12 \), we can conclude that:
\[ \frac{10}{15} > \frac{-12}{15} \]

### Step 6: Conclusion
Thus, \( \frac{2}{3} \) is greater than \( \frac{-4}{5} \).

### Final Answer
The larger number is \( \frac{2}{3} \).

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