Adding Three or More Fractions
Adding three or more fractions requires finding a common denominator for all fractions, renaming each as an equivalent fraction with that denominator, then adding all numerators while keeping the denominator. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students find the LCD of all denominators at once, convert each fraction, and simplify the result. For 1/2 + 1/3 + 1/4: LCD = 12; rename as 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12. If the sum is an improper fraction, convert it to a mixed number and reduce the fraction part to lowest terms.
Key Concepts
New Concept To add three or more fractions, we find a common denominator for all the fractions being added. Once we determine a common denominator, we can rename the fractions and add. What’s next This is just the beginning. Next, you'll walk through worked examples for adding both proper fractions and mixed numbers, putting this core concept into practice.
Common Questions
What is the first step when adding three or more fractions?
Find the Least Common Denominator (LCD) of all the fractions. The LCD is the LCM of all the denominators.
Add 1/2 + 1/3 + 1/6.
LCD of 2, 3, and 6 is 6. Rename: 3/6 + 2/6 + 1/6 = 6/6 = 1.
Add 1/2 + 1/3 + 1/4.
LCD = 12. Rename: 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12.
Do you need a different process for adding three fractions versus two?
No. The process is identical—find the LCD for all denominators, rename all fractions, then add numerators. Having more fractions simply means more renaming steps.
How do you simplify the sum after adding three fractions?
If the result is an improper fraction, divide numerator by denominator to get a mixed number. Then reduce the fractional part by its GCF.