Common Denominators, Part 2
Common Denominators Part 2 extends fraction addition and subtraction to more complex cases in Grade 6 Saxon Math Course 1, including fractions with larger denominators where listing multiples requires more steps. An alternative method uses prime factorization to find the LCD directly: for 5/12 and 7/18, 12 = 2² × 3 and 18 = 2 × 3², so LCD = 2² × 3² = 36. Convert: 5/12 = 15/36 and 7/18 = 14/36, then add or subtract. Mastering both listing and prime-factorization LCD methods handles all fraction computation scenarios.
Key Concepts
New Concept To add, subtract, or compare fractions with unlike denominators, we must rename them to have a common denominator, often using their least common multiple. <br <br To rename a fraction, we multiply it by a fraction equal to 1. What’s next This is the core technique for handling unlike fractions. Next, you’ll apply this concept through worked examples on addition, subtraction, and comparison problems.
Common Questions
How do you find LCD using prime factorization?
Factorize each denominator. Take the highest power of each prime factor that appears. Multiply those together for the LCD.
Find the LCD of 5/12 and 7/18.
12 = 2² × 3, 18 = 2 × 3². LCD = 2² × 3² = 36.
Convert 5/12 and 7/18 to 36ths, then subtract.
5/12 = 15/36, 7/18 = 14/36. 15/36 − 14/36 = 1/36.
When should you use prime factorization over listing multiples to find LCD?
For larger or less obvious denominators, prime factorization is faster and more systematic than listing many multiples.
What is the LCD of 1/6 and 1/9?
6 = 2 × 3, 9 = 3². LCD = 2 × 3² = 18.