Here is how I would approach similar problems:
Solution: [Step 1] 5 2/3-3 1/6= [Step 2] 17/3-19/6= [Step 3] 34/6-19/6= [Step 4] 15/6= [Step 5] 5/2= [Step 6] 2 1/2
Step 1: This is the question
Step 2: Convert the mixed numbers (eg 5 2/3 which have whole number '5', in this case, in front of a proper fraction: which is '2/3' in this case because numerator is smaller than denominator of the fraction) into improper fractions (eg 17/3 which have the numerator [top number] bigger than denominator [bottom number of a fraction] )
Common question: How Do I convert mixed numbers into improper fraction?
5 2/3 ----> Multiply the whole number '5' with denominator '3' and add that number with the numerator '2'. What number do you get? '17' ------> Now this is the new numerator for the improper fraction you want. The fraction has the same denominator as the mixed number ' 3'
So the improper fraction you have is '17/3' ----TADAAA!
Convert 3 1/6 in the same manner and you will get -----> '19/6'
Step 3: Subtract 19/6 from 17/3 -----> 17/3 - 19/6 .......But wait, notice that the denominators are not the same!!!!!!!!!!!!!!!!!!!!! So you cannot subtract these fractions until you have the same numbers in the denominators of the fractions you are subtracting.
What do you do?
Well you realize that 3 can multiply with 2 and convert to 6! So you can conver the first fraction to have the same denominator as the second fraction '19/6'
Remember that when you multiply the denominator of a fraction to convert it into another denominator, you have to use the same multiplying number with the numerator.
So >>>>>>>>>>>>>> (17/3) X (2/2) = 34/6
NOW you can subtract the improper fractions, where the first improper fraction (17/3) converts into (34/6)
>>>>>...... (34/6) - (19/6) = 15/6 You can stop right here if you want but usually multiple choice answers will express this answer in a mixed number (remember the definition for this? Scroll to Step 1 if you forgot)
Step 5: You realize that '15/6' can be reduced down to a simpler fraction if you divide both numerator and denominator by 3! SO you have (15/6) ÷ (3/3) = 5/2
Step 6: Now 5/2 is an improper fraction in that the numerator is bigger than the denominator. You have a choice. You can leave it like it is or you can convert 5/2 into a mixed number. Most multiple choice tests will convert 5/2 into a mixed number.
How do you convert 5/2 into a mixed number?
Do you remember the times table for 2? Well if you do then you should realize that 4 (multiple of 2) is the closest to the numerator value and is less than or equal to it. What number do you multiply 2 to get to 4?
'2' >>>>>>>So this is the whole number that comes in front of our mixed number
Subtract 4 from 5 and we get 1. So 1/2 is left when you remove a whole number out of 5/2
Your mixed number answer is thus 2 1/2
The reason why I do this in an extended manner is so you can understand the concepts. Practically once you know how to do this problem, you have covered the concepts for a majority of other weird problems. What I did here was section this problem into simpler parts so that you can approach a multiple other problems in maybe not the same way but use the concepts from each step or section and arrange each in various orders.