Answer :
We begin by converting the mixed numbers to improper fractions. The mixed number
[tex]$$103\frac{1}{2}$$[/tex]
can be written as
[tex]$$103\frac{1}{2} = 103 + \frac{1}{2} = \frac{103 \times 2 + 1}{2} = \frac{207}{2}.$$[/tex]
Similarly, the mixed number
[tex]$$197\frac{1}{2}$$[/tex]
becomes
[tex]$$197\frac{1}{2} = 197 + \frac{1}{2} = \frac{197 \times 2 + 1}{2} = \frac{395}{2}.$$[/tex]
Next, we multiply these two numbers:
[tex]$$\frac{207}{2} \times \frac{395}{2}.$$[/tex]
If we were to convert these fractions to decimal form, we have
[tex]$$\frac{207}{2} = 103.5 \quad \text{and} \quad \frac{395}{2} = 197.5.$$[/tex]
Multiplying the two decimals gives:
[tex]$$103.5 \times 197.5 = 20441.25.$$[/tex]
Finally, we multiply this product by 48:
[tex]$$20441.25 \times 48 = 981180.$$[/tex]
Thus, the final answer is
[tex]$$\boxed{981180}.$$[/tex]
[tex]$$103\frac{1}{2}$$[/tex]
can be written as
[tex]$$103\frac{1}{2} = 103 + \frac{1}{2} = \frac{103 \times 2 + 1}{2} = \frac{207}{2}.$$[/tex]
Similarly, the mixed number
[tex]$$197\frac{1}{2}$$[/tex]
becomes
[tex]$$197\frac{1}{2} = 197 + \frac{1}{2} = \frac{197 \times 2 + 1}{2} = \frac{395}{2}.$$[/tex]
Next, we multiply these two numbers:
[tex]$$\frac{207}{2} \times \frac{395}{2}.$$[/tex]
If we were to convert these fractions to decimal form, we have
[tex]$$\frac{207}{2} = 103.5 \quad \text{and} \quad \frac{395}{2} = 197.5.$$[/tex]
Multiplying the two decimals gives:
[tex]$$103.5 \times 197.5 = 20441.25.$$[/tex]
Finally, we multiply this product by 48:
[tex]$$20441.25 \times 48 = 981180.$$[/tex]
Thus, the final answer is
[tex]$$\boxed{981180}.$$[/tex]
