Adding Mixed Numbers with Regrouping

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You can add only fractions together that have the same dennominator, so you must first change each of the two fractions to a common denominator.

Example 1 Suppose you have two mixed numbers 1 2/3 and 3 3/4 to be added together

1	2		3	3
	---	+		---	=		---
	3			4

First you must find common denominators.

Select the denominator of the second fraction (4) and multiply the numerator and denominator of the first fraction (2/3) by 4.

2		4		8
---	x	---	=	---
3		4		12

Select the denominator of the first fraction (3) and multiply the the numerator and denominator of second fraction (3/4) by 3.

3		3		9
---	x	---	=	---
4		3		12

These two fractions (8/12 and 9/12) have common denominators.

Add the two new fractions together:

8		9		17
---	+	---	=	---
12		12		12

So your answer will be:

1	4		3	3		4	17
	---	+		---	=		---
	12			12			12

The answer of 4 and 17/12 is an improper fraction. It must be changed to a mixed number.

Divide 17 by 12. The answer is 1 with a remainder of 5. This means 17/12 equals 1 and 5/12. The whole number 1 must be added to the 4 giving a total of 5 and 5/12.

	17		1	5		4
	---	=		---	+		=
	12			12

5	5
	---
	12