Which is greater in each of the
`(-5)/(6) , (-4)/(3)`

Answer

To determine which of the two rational numbers \(-\frac{5}{6}\) and \(-\frac{4}{3}\) is greater, we will follow these steps:

### Step 1: Identify the Rational Numbers
We have two rational numbers:
1. \(-\frac{5}{6}\)
2. \(-\frac{4}{3}\)

### Step 2: Find a Common Denominator
To compare these two fractions, we need a common denominator. The denominators are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6.

### Step 3: Convert the Fractions
Now, we convert both fractions to have the common denominator of 6.

- The first fraction \(-\frac{5}{6}\) already has the denominator of 6, so it remains \(-\frac{5}{6}\).
- The second fraction \(-\frac{4}{3}\) needs to be converted. We can multiply both the numerator and denominator by 2 to get the denominator of 6:
\[ -\frac{4}{3} = -\frac{4 \times 2}{3 \times 2} = -\frac{8}{6} \]

### Step 4: Compare the Numerators
Now we have:
1. \(-\frac{5}{6}\)
2. \(-\frac{8}{6}\)

Since the denominators are the same, we can compare the numerators:
- The numerators are -5 and -8.

### Step 5: Determine Which is Greater
In the case of negative numbers, the number with the smaller absolute value is greater. Here:
- \(-5\) is greater than \(-8\) because \(|-5| < |-8|\).

### Conclusion
Thus, we conclude that:
\[ -\frac{5}{6} > -\frac{4}{3} \]

### Final Answer
\(-\frac{5}{6}\) is greater than \(-\frac{4}{3}\).

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