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How do I work out this problem:5 2/3 - 3 1/6 ? I know the answer is 2 1/2 but how do I arrive at that answer?

I am trying to prepare for a test and I am just learning how to work fractions.


I would like to thank everyone who answered my question; thank you for your time and attention, for being available and for your detailed responses. I had to crew on it for awhile and looking at more than one approach was also helpful. You are all amazing, thank you for what you do to help other succeed.


Dolores J.

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Rizul N. | UNC-CH Grad For Math and Science TutorUNC-CH Grad For Math and Science Tutor
4.8 4.8 (12 lesson ratings) (12)

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. 

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)

When adding/subtracting fractions, you want to find a common denominator for both fractions and do any necessary operations to change the fractions so that they have the same denominator so that you can add/subtract them with ease.

    5 2/3 - 3 1/6   ==> the two denominators here are 3 and 6; since 6 is a multiple of 3,

                                the common denominator is 6.

Since the second fraction already has a denominator of 6, leave it as is. To change the second fraction in a way that would yield a denominator of 6, you need to multiply both the numerator and denominator of the fraction by the same number. So for the fraction 2/3, since you would need to multiply the denominator by 2 to get 6, you would also multiply the numerator by 2. This is like multiplying the fraction by 2/2 which is equal to 1, which wouldn't change the value of the original fraction since any number multiplied by 1 is equal to iteself. So,

       2/3 · 2/=  2·2/3·2 =  4/6

Replace the fraction in the first term of the problem by the one above:

      5 4/6 - 3 1/6  =  5-3 4-1/6  =  2 3/6  =  2 1/2

Yvonne C. | Yvonne, a versatile tutor. Yvonne, a versatile tutor.

First, have a common denominator for both fractions. In this case, I chose 6 for the common denominator.

5  4/6 - 3  1/6

Then, you subtract the numerators... 4-1=3..... and then subtract the whole numbers...5-3= 2

Keep the demoninators the same, you don't change that .

So now, the answer equals to 2  3/6.

Reduce it and you get 2  1/2.


I understand about 6 being the common denominator but how did we get to 4/6 instead of 2/6? Did you do something to change just that one numerator?

Basically whatever you multiplied the demoninator with, you would multiply the same number with the numerator.

Since I multiplied 3x2 to get 6 as the common demoninator, I would do the same to the numerator: 2 (your numerator) x 2(the # you multiplied to get the common demoninator) = 4.

and so, your fraction would be 4/6.