Hi!

This is simpler than it seems.

. If I add the fraction to 4/9, I need to find a common denominator. The smallest common denominator I could use is 18.

So we need to see which fractions would need 18 as the LCM ( least common Multiple).

Let's look at the options.

7/8-- 8 and 9 have nothing in common until you get to 72 ( 8x9), so we can exclude this option.

2/3 and 1/3-- 3 and 9 have 9 in common, so we know we don't need to find the fraction over 18. We can exclude these options as well.

7/9-- The denominator is already the same! This one is easy to exclude.

3/4-- 4 and 9 have nothing in common until you get to 36 ( 8x9), so we can exclude this option.

Now we have 1/2, 1.6 and 5/6 left

2, and 6 will both find their LCD with 9 at 18 ( 2x9 and 6x3)

BUT we can still exclude more fractions!

The second part of the problem says

. If you add 4/9 to my fraction, the sum is an improper fraction or a mixed number.

This means your answer + 4/9 MUST be more than one. We can say that 4/9 is just under 1/2 half, so we know the fraction we choose must be MORE than 1/2.

Now we can eliminate 1/2 and 1/6

We are left with 5/6. Let's check and make sure it works,

5/6 + 4/9 = (x3) 5/6 + 4/9 (x2) = 15/18 + 8/18= 23/18 << this is an improper fraction! If we write it as 1 5/18 we have a mixed number.

So 5/6 satisfies the requirements of the problem!