-38/63 :1 8/49

To solve the expression \(-\frac{38}{63} : 1 \frac{8}{49}\), we will follow these steps:

1. Convert the mixed number to an improper fraction: \[ 1 \frac{8}{49} = \frac{49 \times 1 + 8}{49} = \frac{49 + 8}{49} = \frac{57}{49} \]

2. Rewrite the division as multiplication by the reciprocal: \[ -\frac{38}{63} : \frac{57}{49} = -\frac{38}{63} \times \frac{49}{57} \]

3. Multiply the fractions: \[ -\frac{38 \times 49}{63 \times 57} \]

4. Calculate the numerator and denominator:

   • Numerator: \(38 \times 49 = 1862\)
   • Denominator: \(63 \times 57 = 3591\)

   So, we have: \[ -\frac{1862}{3591} \]

5. Simplify the fraction if possible: We need to check if there are any common factors between \(1862\) and \(3591\).

   The GCD (Greatest Common Divisor) of \(1862\) and \(3591\) is \(1\), which means it cannot be simplified further.

Therefore, the result of the expression \(-\frac{38}{63} : 1 \frac{8}{49}\) is: \[ -\frac{1862}{3591} \]