Answer:
(a)
![4(1)/(5)](https://img.qammunity.org/2021/formulas/mathematics/college/ppwozrk830si9obsi9cubvllc39ref7an5.png)
(b)
![7(7)/(24)](https://img.qammunity.org/2021/formulas/mathematics/high-school/330edf9i80gkhbrigc0by4flz5o2bv4q0j.png)
Explanation:
One way of operating with mixed numbers is to first convert them into improper fractions, and operate with them following the simple rules of fraction multiplication, and at the end convert the answer into mixed number.
(a) For this operation let's first convert
into an improper fraction:
![5(2)/(5) =5+(2)/(5) =(25)/(5) +(2)/(5) =(27)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/bg3go16nttv3kq7lxdwycjbxu5y446g9k5.png)
Now perform the requested operation:
![(7)/(9) \,*\,(27)/(5) =(189)/(45) =(21)/(5) =4(1)/(5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/4m28eqkqjasc7kjepakfbo2fcenabonitd.png)
(b) Start by converting both mixed numbers into improper fractions and then operate as indicated:
![1(3)/(4) =(4+3)/(4) =(7)/(4) \\4(1)/(6) =(24+1)/(6) =(25)/(6)](https://img.qammunity.org/2021/formulas/mathematics/high-school/ihz9j45mns7trklfoj7f16q79pi51q93fy.png)
![(7)/(4) *(25)/(6) =(175)/(24) =7(7)/(24)](https://img.qammunity.org/2021/formulas/mathematics/high-school/kghhw4n9edhase9glhmuatfx5ihw9w3cd9.png)