Here is your equation:
[tex]1 \frac{1}{2} \times 4 \frac{3}{4}[/tex]
You're going to be multiplying two mixed numbers. Since it's hard to multiply two mixed numbers together, change both to improper fractions.
To change a mixed number into an improper fraction, multiply the denominator, which is the bottom number, by the whole number. Then add the numerator, which is the top number, to the product and keep the denominator the same.
[tex]1 \frac{1}{2} \rightarrow \frac{3}{2}[/tex]
[tex]4 \frac{3}{4} \rightarrow \frac{19}{4}[/tex]
Here is your new equation:
[tex]\frac{3}{2} \times \frac{19}{4}[/tex]
Multiply:
[tex]\frac{3}{2} \times \frac{19}{4} = \frac{57}{8}[/tex]
Simplify:
[tex]\frac{57}{8} \rightarrow 7 \frac{1}{8}[/tex]
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[tex]\framebox{Your answer is $\dfrac{57}{8}$ or 7 $\dfrac{1}{8}$}[/tex]
If you have any questions, feel free to ask in the comments! :)