Explanation:
Let's turn each mixed fraction into an improper fraction.
![1 (1)/(4) = (4)/(4) + (1)/(4) = (5)/(4)](https://img.qammunity.org/2023/formulas/mathematics/high-school/az0d81wilbig2qdega8holoaxuqyexakof.png)
![2 (1)/(5) = (5)/(5) + (5)/(5) + (1)/(5) = (11)/(5)](https://img.qammunity.org/2023/formulas/mathematics/high-school/j44z1ejczfkk4j2s8jogori0rr0xrybs8y.png)
We'll use 11/5 twice.
Multiply:
![(5)/(4) * (11)/(5) = (55)/(20)](https://img.qammunity.org/2023/formulas/mathematics/high-school/qg5pkg4fucuazsfqsi6kaa7ui975k3bxo6.png)
![(55)/(20) = (20)/(20) + (20)/(20) + (15)/(20) = 2 (15 / 5)/(20 / 5) = 2 (3)/(4)](https://img.qammunity.org/2023/formulas/mathematics/high-school/o5dh3tf1gqpsiqxvf1r2fyxzzgfvltt2i5.png)
Multiply the Second problem:
![(5)/(6)*(11)/(5)=(55)/(30)](https://img.qammunity.org/2023/formulas/mathematics/high-school/ta70rbf6cwozjw04op4a81elp90bierq4t.png)
![(55)/(30) =(30)/(30) +(25)/(30)= 1 (25 / 5)/(30 / 5) = 1 (5)/(6)](https://img.qammunity.org/2023/formulas/mathematics/high-school/pvas7xqqrwg0pezdtdzzh7ss91lrwmfy78.png)
Compare:
![2 (3)/(4) > 1(5)/(6)](https://img.qammunity.org/2023/formulas/mathematics/high-school/dnzlfb4ryt59w9a7ua65tmveduo5dn24cy.png)
2 3/4 is greater, we can identify this a few ways:
- Decimals, 2 3/4 equals 2.75 while 1 5/6 equals 1.83
- Whole numbers, 2 is greater than 1.
- Improper fractions, 2 3/4 as an improper fraction is 11/4 while 1 5/6 as an improper fraction is 11/6.
Therefore, your answer is >