Answer:
18 3/4
Explanation:
First, we need to convert the mixed numbers into fractions, so:
![\begin{gathered} 12\frac{1}{2}=\frac{(12\times2)+1}{2}=\frac{24+1}{2}=\frac{25}{2} \\ 1\frac{1}{2}=\frac{(1\times2)+1}{2}=\frac{2+1}{2}=\frac{3}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2012%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%2812%5Ctimes2%29%2B1%7D%7B2%7D%3D%5Cfrac%7B24%2B1%7D%7B2%7D%3D%5Cfrac%7B25%7D%7B2%7D%20%5C%5C%201%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B%281%5Ctimes2%29%2B1%7D%7B2%7D%3D%5Cfrac%7B2%2B1%7D%7B2%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%5Cend%7Bgathered%7D)
It means that Shamika worked 25/2 hours last week and this week she worked 3/2 times the hours worked last week. So, to know the number of hours worked this week we need to multiply 25/2 by 3/2 to get:
![\frac{25}{2}\times\frac{3}{2}=\frac{25\times3}{2\times2}=\frac{75}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B2%7D%5Ctimes%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B25%5Ctimes3%7D%7B2%5Ctimes2%7D%3D%5Cfrac%7B75%7D%7B4%7D)
Then, 75/4 as a mixed number is equal to:
![\frac{75}{4}=18\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7B4%7D%3D18%5Cfrac%7B3%7D%7B4%7D)
Because when we divide 75 by 4, we get 18 as a quotient and 3 as a remainder.
Therefore, she worked 18 3/4 hours this week.