Adding and subtracting fractions

July 23, 2021

Adding and subtracting fractions, especially heterogeneous ones (with unlike denominators), is often a challenging concept for students since there is a lot of prerequisite knowledge involved like fluency with multiplication and division facts, LCM, equivalent fractions, and more.

Before students start with adding and subtracting fractions they need to have a thorough understanding of the concept of fractions with visuals like number lines, shapes, and quantities. They also need to understand mixed numbers and improper fractions and be able to convert mixed numbers to improper fractions and the opposite.

Adding / subtracting homogeneous (like) fractions

Adding and subtracting fractions with like denominators is relatively simpler than adding and subtracting heterogeneous fractions (with unlike denominators) which requires a good understanding of equivalent fractions, prime factorization, and LCM.

We start with adding and subtracting fractions with like denominators using visuals like shapes, number lines, groups.

The challenge with adding fractions with like denominators is converting mixed numbers to improper fractions and the opposite. The students need to be able to convert a mixed number into an improper fraction in order to add or subtract and then turn the answer back to a mixed number. Start with visual examples and let the students figure out the algorithm. This way they will gain a concrete understanding.

Adding / subtracting heterogeneous (unlike) fractions

Adding and subtracting unlike fractions presents a greater challenge however explaining the concept with visuals will help the students understand the need to convert the fractions into a number of parts of the same size in order to add or subtract them.

Fraction bars as well are a great way to help students gain a clear understanding. The students can see which fraction bar can help them express both fractions as a number of equal parts and it’s a great introduction to Lowest Common Multiple.

Students will eventually use the Lowest Common Multiple ( LCM) to solve problems however it is important to visually understand why that works and why it is the most efficient way.

I always like to review the concept of equivalent fractions before diving into adding and subtracting, unlike fractions.

To find the LCM of two numbers the students can use prime factorization, make lists of multiples or use a multiplication table. Practice finding the LCM of numbers with games and fun quizzes. Show the students how to use the multiplication table to find LCM. Prime factorization is often used for greater numbers, however, practicing with smaller numbers will help the students get comfortable with the process.

LCM is not just for adding and subtracting fractions but for comparing unlike fractions as well.

Adding and subtracting mixed numbers that include unlike fractions is a longer process as the students need to convert the mixed numbers into improper fractions to add/subtract.

Practice solving word problems with fractions, like, and unlike to connect learning to real life, challenge your students’ thinking and practice their problem-solving skills.