let's firstly convert the mixed fractions to improper fractions and then multiply.
[tex]\bf \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{9}{2}\cdot \cfrac{5}{2}\implies -\cfrac{9\cdot 5}{2\cdot 2}\implies -\cfrac{45}{4}\implies -11\frac{1}{4}[/tex]
Answer:
The product is [tex]-11\left(\frac{1}{4}\right)[/tex]
Solution:
The first number is [tex]-4 \frac{1}{2}[/tex]
Now if we simplify the first number we get, [tex]-4 \frac{1}{2}=-\left(4+\frac{1}{2}\right)=-4-\frac{1}{2}[/tex]
[tex]=\frac{-4 \times 2-1}{2}=-\frac{9}{2}[/tex]
The second number is [tex]2\left(\frac{1}{2}\right)[/tex]
If we simplify the second number we get, [tex]2 \frac{1}{2}=\frac{2 \times 2+1}{2}=\frac{5}{2}[/tex]
Now the product of both the numbers are,
[tex]-4 \frac{1}{2} \times 2 \frac{1}{2}[/tex]
[tex]\left(-\frac{9}{2}\right) \times \frac{5}{2}[/tex]
[tex]-\left(\frac{9 \times 5}{2 \times 2}\right)[/tex]
[tex]-\left(\frac{45}{4}\right)[/tex]
