Common Denominators, Part 1
Finding a common denominator is required before adding or subtracting fractions with unlike denominators. In Grade 6 Saxon Math Course 1, students find the Least Common Denominator (LCD) by listing multiples of each denominator and identifying the smallest shared multiple. For 3/4 and 5/6, multiples of 4 are 4, 8, 12 and multiples of 6 are 6, 12, so LCD = 12. Convert each fraction: 3/4 = 9/12 and 5/6 = 10/12. Now addition is straightforward: 9/12 + 10/12 = 19/12.
Key Concepts
New Concept To add or subtract fractions that do not have common denominators, we rename one or more of them to form fractions that do have common denominators. What’s next This is the foundation for all fraction arithmetic. Soon, we'll apply this concept through worked examples on adding and subtracting fractions with unlike denominators.
Common Questions
Why do fractions need a common denominator to be added?
You can only add quantities of the same unit. Without the same denominator, fractions represent different-sized parts, making direct addition meaningless.
What is the LCD of 3/4 and 5/6?
Multiples of 4: 4, 8, 12. Multiples of 6: 6, 12. LCD = 12.
How do you convert 3/4 to twelfths?
Multiply numerator and denominator by 3: 3/4 = 9/12.
Add 3/4 + 5/6.
Convert to 9/12 + 10/12 = 19/12 = 1 7/12.
Does changing the denominator change the fraction's value?
No. Multiplying both numerator and denominator by the same non-zero number creates an equivalent fraction with the same value.