MHB Subtracting mixed fractions help

[botswana]

Hi, I'm new. Please bear with me because I'm not familiar with the code of this forum.

I don't know how to enter a mixed fraction correctly, so I'm just going to write it out. Here is the problem:

Four and five-ninths minus 2/3

Can someone explain to me why the answer is three and eight-ninths? I know that's the answer because the textbook I'm using says so, but I haven't been able to figure out why.

 

[MarkFL]

I would convert to improper fractions:

$4\frac{5}{9}-\dfrac{2}{3}=\dfrac{9\cdot4+5}{9}-\dfrac{2}{3}=\dfrac{41}{9}-\dfrac{2}{3}$

Now, get a common denominator:

$$\frac{41}{9}-\frac{2}{3}\cdot\frac{3}{3}=\frac{41}{9}-\frac{6}{9}=\frac{41-6}{9}=\frac{35}{9}$$

Now express as a mixed fraction:

$\dfrac{35}{9}=\dfrac{3\cdot9+8}{9}=3+\dfrac{8}{9}=3\frac{8}{9}$

Does that make sense?