Comparing fractions with different denominators | Fractions | Pre-Algebra | 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.

Key Insights

• ❓ Simplifying fractions can make it easier to compare them.
• ❓ Finding a common denominator is necessary to accurately compare fractions with different denominators.
• 🧑‍🏭 The least common multiple can be used to find a common denominator when the values share no prime factors.
• ❓ Comparing the numerators is sufficient to determine which fraction is greater.

Transcript

Use less than, greater than, or equal to compare the two fractions 21/28, or 21 over 28, and 6/9, or 6 over 9. So there's a bunch of ways to do this. The easiest way is if they had the same denominator, you could just compare the numerators. Unlucky for us, we do not have the same denominator. So what we could do is we can find a common denominator... Read More

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.