Adding Fractions with Unlike Denominators is Complex

Adding and Subtracting Fractions with Unlike Denominators is Difficult

• There are several steps to the process.
• At first it is difficult to tell if the answer is even in the ballpark.
• The magnitude of the sums and differences may not match what students were expecting
• Students have to find common denominators,
• students must learn about prime factors,
• greatest common factors, and
• least common multiples,  AND then 
• make use of this information consistently and accurately 
• as it applies to numbers in the denominator 

Remember, there is evidence that many adults don’t have an intuitive sense that tells them ⅓ is larger than 1/4. 

So, in some ways, learning to add and subtract fractions is like learning to calculate in an entirely new language , upside down, and underwater, while walking on a tightrope.

Concrete Examples Help Students Understand

One way to support young learners is to use concrete examples. Teachers provide a variety of models for students to work with. These include linear models like number lines, lengths of string, ribbon, or tape, and rulers; area models such as equal sections of geometric shapes, tiling imaginary courtyards or swimming pools, and using graph paper; and set models such as days per week, dozens of diamonds, nickels per dollar and other types of collections. Teachers also use volumetric models and lengths of time, or durations, as models for students to use when first learning how to add and subtract fractions. 

Manipulatives and real life examples help students picture what is happening. They can solve the math problem by moving pieces around or drawing a picture.

Slowly Increase the Complexity

Another way to support learners is to begin with the simplest addition and subtraction problems such as when the fractions already have the same denominators. 

The next step is usually to show students that the product of the two denominators will always work as a common denominator. This has the advantage of reminding students that multiplying by one does not change the value of the number. Students get into the habit of making sure their answers are expressed in the simplest form.

Next, students are asked to take a giant step up from using like denominators or products as common denominators. In order to continue learning how to add or subtract fractions, students have to be able to calculate least common denominators.

There is a smaller step that you can use to help your students understand the idea of Least Common Denominator LCD before they have to deal with prime numbers. Introducing one new idea at a time reduces the complexity and allows students to move at their own pace. A small subgroup of number pairs, when used as denominators in fractions, have the extremely useful property that  the difference between their unit fractions is also their least common denominator LCD.

Discover how to help your students make sense of prime factors, GCF, LCM, and LCD.

Find out more about this special group of number pairs that let students find the LCD by using manipulatives.