## Grade 5 Math: How to add and subtract fractions with different denominators, or unlike denominators

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### Adding and Subtracting Fractions with Unlike Denominators

This series of lessons describes how to add and subtract fractions and mixed numbers with unlike denominators.

All the lessons in this series represent fractions as distances on a number line rather than concrete objects. The rationale behind this approach is well-established through research, and is currently prescribed in the Common Core State Standards.

### Finding a Common Denominator: General Strategy

Lesson 1 of the series covers the most general strategy for finding a common denominator – multiplying the denominators. This general strategy applies to any situation in which two fractions with different denominators are added or subtracted.

### Finding a Common Denominator: One Denominator a Factor of the Other

Lesson 2 covers how to add fractions when one denominator is a factor of the other. In this case, there is no need to multiply the denominators since one denominator is already the product of the other denominator and some unknown factor. Students learn this as a special case that applies only when one denominator is a factor of the other.

### Least Common Multiple

Lesson 3 covers how to find the Least Common Multiple of two denominators. This Lesson is preparation for the next lesson in which students learn how to use the Least Common Multiple as the common denominator.

### Least Common Multiple as a Common Denominator

Lesson 4 covers how to use the Least Common Multiple as the common denominator to add or subtract fractions. Students are taught that this is an alternative to the general strategy of multiplying the denominators to find the common denominator, but is not a required approach.

### Adding and Subtracting Fractions with Unlike (Different) Denominators

Lesson 5 covers adding and subtracting fractions using any method to find the common denominators. Students are required to add and subtract two fractions with unlike (different) denominators by first finding a common denominator. They are allowed to use any method that is applicable.

### Adding and Subtracting Mixed Numbers with Unlike Denominators

Lesson 6 covers adding and subtracting mixed numbers. Students are taught to first convert the mixed numbers to improper fractions, then to find a common denominator for the fractions before adding or subtracting.

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