Subtracting Mixed Fractions

A mixed fraction is a fraction that consists of a whole part and a fraction part. For example, 3 ¾ inthis mixed fraction 3 is the whole part and ¾ is the fraction part. Before learning the steps involved in subtracting mixed fractions it is important to learn how to convert a mixed fraction into an improper fraction. Given a mixed fraction 3 1/4 let us convert it to an improper fraction; first the product of the  denominator and the whole part is calculated, 3 x 4 which gives 12, to this product the numerator 1 is added 12+1 to give 13, this number thus obtained is the numerator of the improper fraction and the denominator remains the same thus giving the required improper fraction 13/14. Once the concept of converting the mixed fraction to improper fraction is clear we can proceed to the steps involved in the subtraction of mixed fractions. Consider the subtraction of mixed fractions 4 ¾ - 2 ¼, here first convert the mixed fractions to improper fractions. 4 ¾ is (4x4 + 3)/4 = 19/4 and 2 ¼ is (4x2 +1)/4= 9/4. This gives19/4 – 9/4, as we can see the denominators are the same so we just need to subtract the numerators;(19-9)/4 = 10/4 = 5/2 (reduced fraction), this is in the improper fraction form which we convert to mixed form 2 1/2.


Another method used in the subtraction mixed fractions is to first write the mixed fractions as a sumof the whole part and the fraction part and then the whole part and the fraction part are simplified separately. Finally the whole part and fraction part are combined to get the required mixed fraction. For example, 4 ¾ - 2 ¼ can be written as 4 + ¾ - (2 + ¼) = 4 +3/4- 2 – ¼ = (4-2) + (3/4- ¼) = 2 + 2/4 which canbe written as 2 2/4 on simplification of the fraction part which is allowed, 2 ½ is the final answer. 


 The mixed fractions at times have different denominators, in such cases the mixed fractions subtractions involves the following steps:

 • first convert mixed fractions to improper fractions, 

• then make the denominators of the fractions same, 

• subtract the numerator part , 

• simplify if required and finally write in mixed form.


 For example, 6 ½ - 3 1/6 = 13/2 – 19/6, to make the denominators same the common denominator is 6,13x3/2x3 – 19/6=39/6 – 19/6=(39-19)/6=20/6, reducing the fraction we get 10/3 which is 3 1/3(mixedform)