Finding common denominators | Fractions | Pre-Algebra | Khan Academy

TL;DR

Learn how to find the least common denominator (LCD) and rewrite fractions using it.

Transcript

We're asked to rewrite the following two fractions as fractions with a least common denominator. So a least common denominator for two fractions is really just going to be the least common multiple of both of these denominators over here. And the value of doing that is then if you can make these a common denominator, then you can add the two fracti... Read More

Key Insights

• ❓ The least common denominator (LCD) is the least common multiple of the denominators of two fractions.
• 👂 The multiples of each denominator can be listed to find their smallest common multiple.
• ❓ Another method to find the LCD is through prime factorization.
• 🧑‍🏭 Multiplying the numerator and denominator by the same factor preserves the value of a fraction.
• 🪜 The least common denominator is useful for adding or comparing fractions.
• ❓ Fractions can be rewritten using different denominators, but the LCD simplifies calculation.
• 🧑‍🏭 The prime factorization of the denominators helps determine the required factors for the LCD.

Questions & Answers

Q: What is the purpose of finding the least common denominator (LCD) for fractions?

The LCD allows fractions to have a common denominator, enabling easy addition or comparison between the fractions.

Q: How can the LCD be found using prime factorization?

The prime factorization of the denominators is analyzed to find the common prime factors. The LCD is then determined by multiplying these factors together.

Q: Can fractions be rewritten using a different least common denominator?

Yes, fractions can be rewritten using different denominators, but the least common denominator is preferred to simplify calculations and avoid larger numbers.

Q: How does multiplying the numerator and denominator by the same factor preserve the value of a fraction?

Multiplying the numerator and denominator by the same factor is equivalent to multiplying the fraction by 1, which does not change its value.

Summary & Key Takeaways

• The least common denominator (LCD) is the least common multiple of the denominators of two fractions.

• The multiples of 6 and 8 are found to determine their smallest common multiple, which is 24 in this case.

• To rewrite fractions with the LCD, the numerator and denominator are multiplied by the same factor.