The operation we have to solve is:
[tex]1\frac{7}{9}\div\frac{4}{5}[/tex]The steps to solve are the following:
Step 1. Convert the first mixed number 1 7/9 to a fraction.
We convert 1 7/9 to a fraction following the general rule:
[tex]A\frac{b}{c}=\frac{A\times c+b}{c}[/tex]Applying this to 1 7/9:
[tex]1\frac{7}{9}=\frac{1\times9+7}{9}[/tex]which is equal to:
[tex]1\frac{7}{9}=\frac{16}{9}[/tex]Substituting this, the operation we have to solve is:
[tex]\frac{17}{9}\div\frac{4}{5}[/tex]Step 2. Now we apply the following rule to divide fractions:
[tex]\frac{a}{b}\div\frac{d}{c}=\frac{a\times c}{b\times d}[/tex]And the result is:
[tex]\frac{17}{9}\div\frac{4}{5}=\frac{17\times5}{9\times4}[/tex]which is equal to:
[tex]\frac{17}{9}\div\frac{4}{5}=\frac{85}{36}[/tex]Step 3. Convert the result to a mixed number.
In step 2 we got 85/36 as a result, but we can convert that fraction to a mixed number considering that 36 fits two times in the number 85 (because 36x2=72) and we have 85-72=13 out 36 left:
[tex]\frac{85}{36}=2\frac{13}{36}[/tex]Answer:
[tex]2\frac{13}{36}[/tex]