Which is greater in each of the
`-3 (2)/(7) , - 3 (4)/(5)`

Answer

To determine which of the two rational numbers, \(-3 \frac{2}{7}\) and \(-3 \frac{4}{5}\), is greater, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers to improper fractions.

1. For \(-3 \frac{2}{7}\):
- Multiply the whole number (3) by the denominator (7): \(3 \times 7 = 21\)
- Add the numerator (2): \(21 + 2 = 23\)
- Therefore, \(-3 \frac{2}{7} = -\frac{23}{7}\)

2. For \(-3 \frac{4}{5}\):
- Multiply the whole number (3) by the denominator (5): \(3 \times 5 = 15\)
- Add the numerator (4): \(15 + 4 = 19\)
- Therefore, \(-3 \frac{4}{5} = -\frac{19}{5}\)

### Step 2: Find a Common Denominator
Next, we need to find a common denominator to compare the two fractions. The denominators are 7 and 5.

- The least common multiple (LCM) of 7 and 5 is \(35\).

### Step 3: Convert Fractions to Have the Same Denominator
Now, we convert both fractions to have the common denominator of 35.

1. For \(-\frac{23}{7}\):
- Multiply both the numerator and denominator by 5:
\[ -\frac{23 \times 5}{7 \times 5} = -\frac{115}{35} \]

2. For \(-\frac{19}{5}\):
- Multiply both the numerator and denominator by 7:
\[ -\frac{19 \times 7}{5 \times 7} = -\frac{133}{35} \]

### Step 4: Compare the Two Fractions
Now we compare \(-\frac{115}{35}\) and \(-\frac{133}{35}\).

- Since both fractions have the same denominator, we can compare the numerators:
- \(-115\) and \(-133\)

### Step 5: Determine Which is Greater
- In the number line, a number that is less negative is greater. Here, \(-115\) is greater than \(-133\).

### Conclusion
Thus, we conclude that:
\[ -\frac{115}{35} > -\frac{133}{35} \]
This implies:
\[ -3 \frac{2}{7} > -3 \frac{4}{5} \]

### Final Answer
Therefore, \(-3 \frac{2}{7}\) is greater than \(-3 \frac{4}{5}\).

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