Fractions / Adding Fractions with Unlike Denominators

Understanding

As students explore the concept of adding fractions, they should begin to see that a common denominator will always be the product of the two denominators.

What to look for

If the denominators do not have a common factor, the rectangles in both unit squares are congruent. If the denominators have a common factor, however, the rectangles are not necessarily congruent, as displayed in the file.

Sample Assessment

If one part of a recipe calls for  (2/3) cup of milk and another part of the same recipe calls for (3/4) cup of milk, how much milk do you need all together for the recipe? 

Answer:  (17/12) cups.

The Big Idea

Fractions with unlike denominators need to be re-expressed in terms of equivalent fractions with a new common denominator.

What are the students doing?

Students will use unit squares to add fractions with unlike denominators. Recall why it is possible to add the two fractions when the denominators are the same.

What is the teacher doing?

Finding a least common denominator is not necessary and, in fact, can lead to confusion for students, obscuring the goal of adding fractions.