# how would you sloved this problem? 3 1/4 - 1 5/6 =

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The first thing to understand in order to solve this problem is one can only subtract like units. The denominator( bottom number) in a fraction is the unit, it names the size of the pieces while the numerator ( top number) names the quantity ( how many) of the pieces.
So in the problem 3 1/4 - 1 5/6, you must name the two fractional parts with the same name. You do this by using equivalent fractions. One way to find equivalent fractions is to find the least common denominator. To find the least common denominator, you must find the least common multiple of the two denominators. Consider the multiples (x 1, x 2, x 3, etc.) of 4 and 6. The least multiple that is the same is 12.
So if you draw a model of a whole divided into 1/4s, shade 1/4, then divide the same whole into 1/12s, you will see that there are 3/12 inside of 1/4. Draw a model of one whole divided into 1/6s. Shade 5/6, then divided the same whole into 1/12s. You will see that there are 2/12 inside of each 1/6, so there are a total of 10/12 inside of 5/6.
Now, when you consider subtracting 10/12 from 3/12, you will realize that 3/12 is not enough to subtract 10/12 from. At this point you can either take 1 whole from the 3 wholes, name it as 12/12, combine it with the 3/12 to get 13/12 from which you can easily subtract 10/12 and then subtract 1 whole from the remaining 2 wholes to get a total of 1 3/12 which is equivalent to 1 1/4....OR
You can convert both mixed numbers to improper fractions and then subtract and simplify your answer.

Notice that the problem involves subtraction of two mixed fractions, hence you need to convert these mixed fractions into improper fractions such that:

`3 1/4 = (3*4+1)/4 = 13/4`

`1 5/6 = (1*6 + 5)/6 = 11/6`

Hence you need to find the difference between `13/4 - 11/6` such that:

`13/4 - 11/6`

You need to bring these fractions to a common denominator such that:

`13*3/12 - 11*2/12 = (39 - 22)/12 = 17/12`

You need to convert the improper fraction `17/12` into a mixed fraction such that `17/12 = 1 5/12`

**Hence, evaluating subtraction of mixed fractions yields `3 1/4 - 1 5/6 = 1 5/12` .**