Adding Simple Fractions with Conversion to Mixed Numbers

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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.

The only time you need to convert is when the numerator is larger than a denonminator.

Example 1 Suppose you have two fractions 4/7 and 5/7 to be added together

4		5		9
---	+	---	=	---
7		7		7

The answer is an improper fraction. This means the top number is larger than the bottom number. To convert to a mixed number, divide the top (numerator) by the bottom (denominator). The remainder should be placed over the denominator for the fraction left over.

9 divided by 7 equals 1 with a remainder of 2. The mixed number is 1 and 2/7.

For more practice on converting to mixed numbers go to converting improper fractions to mixed numbers.

Example 2 Suppose you have the fractions 5/8 and 10/11 to be added together.

5		10		?
---	+	---	=	---
8		11		?

Select the denominator of the second fraction (11) and multiply the numerator and denominator of the first fraction (5/8) by 11:

11		5		55
---	x	---	=	---
11		8		88

Select the denominator of the first fraction (8) and multiply the second fraction (10/11) by that number for both the numerator and denominator:

8		10		80
---	x	---	=	---
8		11		88

These two fractions (55/88 and 80/88) have common denominators.

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

55		80		135
---	x	---	=	---
88		88		88

DO NOT add the denominators!

Your answer is an improper fraction. The numerator is larger than the denominator. Divide the numerator by the denominator. Put the remainder over the denominator. 135 divided by 88 is 1 with a remainder of 47. The answer would be 1 and 47/88. The fraction 47/88 cannont be reduced.

Good luck in adding fractions with conversion to a mixed number.