Common Denominators
Common Denominators is a skill on Pengi from Lesson 13: Adding and Subtracting Fractions and Mixed Numbers in Saxon Math, Course 3.
Key Concepts
Property When two fractions have the same denominator, we say they have common denominators . To create them, find an equivalent fraction by multiplying by a form of 1, such as $\frac{a}{b} \cdot \frac{c}{c} = \frac{ac}{bc}$.
Examples To add $\frac{2}{3} + \frac{3}{4}$, use 12 as the common denominator: $\frac{2}{3} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{3}{3} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12}$. To subtract $\frac{3}{4} \frac{1}{6}$, the least common denominator is 12: $\frac{3}{4} \cdot \frac{3}{3} \frac{1}{6} \cdot \frac{2}{2} = \frac{9}{12} \frac{2}{12} = \frac{7}{12}$. To add $\frac{1}{2} + \frac{1}{5}$, the common denominator is 10: $\frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{2}{2} = \frac{5}{10} + \frac{2}{10} = \frac{7}{10}$.
Explanation You can't add fractions with different slice sizes! To make it work, you must find a 'common denominator' so the pieces are the same size. A quick trick is to multiply the two different denominators to find a new one that works for both. This lets you add or subtract them fairly.
Common Questions
What is Common Denominators?
Common Denominators is a skill on Pengi from Lesson 13: Adding and Subtracting Fractions and Mixed Numbers in Saxon Math, Course 3.
What grade level is Common Denominators for?
Common Denominators is part of the Grade 8 Math curriculum, covered in Saxon Math, Course 3. It is designed for students studying Math at the Grade 8 level.
How can I learn Common Denominators?
Pengi offers an AI-guided lesson for Common Denominators that walks you through the key concepts step by step. The lesson is aligned to Saxon Math, Course 3 so the content matches what you see in class.
How do I practice Common Denominators?
After learning the concept, use the Practice mode to work through targeted exercises on Common Denominators. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Common Denominators?
Common Denominators is covered in Saxon Math, Course 3, specifically in Chapter 2: Number & Operations • Geometry under Lesson 13: Adding and Subtracting Fractions and Mixed Numbers. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Common Denominators free to study on Pengi?
Yes, the core Learn and Practice modes for Common Denominators are available for free on Pengi. No credit card is required to start studying.