Fill in the boxes the correct symbol out of `gt,lt and =.`
`(-8)/(5) square (-7)/(4)`

Answer

To solve the problem of comparing the two rational numbers \(-\frac{8}{5}\) and \(-\frac{7}{4}\), we will follow these steps:

### Step 1: Identify the Rational Numbers
We have two rational numbers to compare:
- \(A = -\frac{8}{5}\)
- \(B = -\frac{7}{4}\)

### Step 2: Find a Common Denominator
To compare the two fractions, we need a common denominator. The denominators are 5 and 4. The least common multiple (LCM) of 5 and 4 is 20.

### Step 3: Convert Each Fraction to Have the Common Denominator
Now we will convert both fractions to have the denominator of 20.

For \(A = -\frac{8}{5}\):
\[ -\frac{8}{5} = -\frac{8 \times 4}{5 \times 4} = -\frac{32}{20} \]

For \(B = -\frac{7}{4}\):
\[ -\frac{7}{4} = -\frac{7 \times 5}{4 \times 5} = -\frac{35}{20} \]

### Step 4: Compare the Numerators
Now we have:
- \(A = -\frac{32}{20}\)
- \(B = -\frac{35}{20}\)

Since the denominators are the same, we can compare the numerators:
- \(-32\) (from \(A\)) and \(-35\) (from \(B\))

### Step 5: Determine Which is Greater
In negative numbers, a number with a smaller absolute value is greater. Here, \(-32\) is greater than \(-35\) because:
\[ -32 > -35 \]

### Step 6: Write the Comparison
Thus, we can conclude:
\[ -\frac{8}{5} > -\frac{7}{4} \]

### Final Answer
The correct symbol to fill in the box is:
\[ -\frac{8}{5} \quad \text{gt} \quad -\frac{7}{4} \]

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