First, you must take account of PEMDAS. In this case, the division part comes first, then the subtraction next.
Before dividing 2 4/9 by 4 ⅔, make both of the fractions into improper fractions.
2×9=18, 18+4=22 -> 22/9
4×3=12, 12+2=14 -> 14/3
Next, you need to make sure both have the same denominator. Since the LCM is 9, 22/9 does not need to be changed but 14/3 does.
3×3=9
14×3=42;
42/9
Now divide both fractions (omit the denominators, dividing both numerators will become a fraction).
22÷42=11÷21=11/21
Now that you gotten 11/21 by dividing, now you must subtract 3/7 from 11/21. This should be easier since there are no mixed numbers this time, but you must change the form of the fraction for both denominators to be the same by finding the LCM again, which is 21.
Multiply 7 by 3 to get 21, and 3 by 3 to get 9. (9/21)
Now, subtract.
11/21–9/21=2/21.
There’s no need for simplifying since it’s in the simplest form.
Therefore, your answer is 2/21.
