First you need to make all the fractions have the same denominator - the bottom number. You're working with thirds, sixths and ninths. All of those can be converted to 18ths (3, 6 and 9 all can go into 18). Let's convert 1/3 to ?/18 first. To change the denominator (3) to 18, you multiply it by 6, so you also multiply the numerator (number on the top) by 6. So 1/3 = 6/18. Convert 5/6 next. To change the denominator (6) to 18 you multiply by 3, so do the same with the numerator (in this case 5). 5 x 3 = 15, so 5/6 = 15/18. Convert the final number 2/9 to ?/18. To change the denominator 9 to 18, you multiply by 2, so do the same thing with the numerator. 2 x 2 = 4, so 2/9 = 4/18.

Now they are all converted to 18ths, you can do the addition and subtraction. With the conversions, we now show the problem as

6/18 + 15/18 - 4/18 = ? The numerators are added or subtracted: 6 + 15 - 4 = 17. The denominator is 18 for all the fractions. So your answer is 17/18.

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