Adding Fractions with Different Denominators

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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 fractions 2/3 and 3/4 to be added together

2		3		?
---	+	---	=	---
3		4		?

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

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

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

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

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

Add the numerators of the two new fractions together but do not add the denominators together

8		3		11
---	+	---	=	---
12		12		12

Example 2 Suppose you have the fractions 3/5 and 4/7 to be added together

3		4		?
---	+	---	=	---
5		7		?

Select the denominator of the second fraction (7) and multiply the numerator and denominator of the first fraction (3/5) by that number:

7		3		21
---	x	---	=	---
7		5		35

Select the denominator of the first fraction (5) and multiply the numerator and denominator of the second fraction (4/7) by that number:

5		4		20
---	x	---	=	---
5		7		35

These two fractions (21/35 and 20/35) have common denominators.

We can now add the two new fractions together since they have a common denominator.

21		20		41
---	x	---	=	---
35		35		35

Add the numerators of the two new fractions together but do not add the denominators together

Since 41/35 is improper it can be changed to a mixed number:

Change 41/35 to a mixed number

41 needs to be divided by 35. The whole number is 1 since 35 goes into 41 one time. The remainder is 6. The fraction left over would be 6/35 since 35 is the divisor.

Good luck in adding fractions with different denominators.