The patel family went apple picking. the number of red apples they picked was 2 2/9 times the number of green apples they picked. if they picked 45 green, how many red apples did they pick?

100 
I first made 45 a fraction = 45/1

Then i made 2 2/9 into an improper fraction 

then make my equation

45/1 ×20/9=100

answer is 100 red apples

To solve this, multiply the number of green apples by 2 2/9 since there are 2 2/9 more reds than greens. This would result in this expression:
2 2/9 * 45 
Since you have a mixed fraction, to make things easier (so you can multiply straight across) change 2 2/9 to an improper fraction (multiply 2 by the denominator and add that to the numerator) which would be 20/9. Then, change 45 to a fraction, 45/1 and multiply 45/1 by 20/9. Then, to avoid having to multiply 45 by 20, cross cancel or factor. Since 45 and 9 both have a factor of 9, divide 9 from each. This would simplify to 5/1*20/1. This would then simplify to your 100 red apples.