Comparing fractions with different denominators  Fractions  PreAlgebra  Khan Academy  Summary and Q&A
TL;DR
Comparing fractions 21/28 and 6/9, the simplified versions are 3/4 and 2/3 respectively. After finding a common denominator, it is evident that 3/4 is greater than 2/3.
Questions & Answers
Q: How can the fractions 21/28 and 6/9 be compared?
The fractions can be simplified first. 21/28 simplifies to 3/4 and 6/9 simplifies to 2/3. Then, a common denominator can be found to compare the fractions.
Q: What is the common denominator for 3/4 and 2/3?
The common denominator is the least common multiple of 4 and 3, which is 12. Both fractions can be written with 12 as the denominator.
Q: How can the numerators be compared when the fractions have a common denominator?
After finding the common denominator, only the numerators need to be compared. In this case, 9/12 is greater than 8/12, therefore, 3/4 is greater than 2/3.
Q: Can the fractions 21/28 and 6/9 be compared without simplifying?
Yes, it is possible to compare the fractions without simplifying first. Find the least common multiple of the denominators, which is 252, and convert both fractions to have 252 as the denominator. Comparing the numerators, 189 is greater than 168, indicating that 21/28 is greater than 6/9.
Summary & Key Takeaways

The fractions 21/28 and 6/9 are compared to determine which is greater.

Simplifying the fractions, 21/28 becomes 3/4 and 6/9 becomes 2/3.

Finding a common denominator (12), the fractions become 9/12 and 8/12.

Comparing the numerators, 9/12 is shown to be greater than 8/12.